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  • 1.
    Eskandari, Setareh
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik. Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.
    Abkar, Ali
    Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.
    Åhag, Per
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Perälä, Antti
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sub-Hilbert relation for Fock-Sobolev type spaces2022Ingår i: New York Journal of Mathematics, E-ISSN 1076-9803, Vol. 28, s. 958-969Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, two specific sub-Hilbert spaces are studied. They arise from the action of a Toeplitz operator on Fock–Sobolev type spaces, in-duced by a general Gaussian type weight. The argument is based on analysing the reproducing kernel of the corresponding sub-Hilbert space.

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  • 2. Gidlund, Mikael
    et al.
    Åhag, Per
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Performance of Opportunistic Scheduling Schemes for MIMO-OFDM Wireless LANs2008Ingår i: IEEE Conference on Local Computer Networks (LCN'08), 14-17 Oct. 2008, Montreal, Canada, 2008Konferensbidrag (Refereegranskat)
  • 3.
    Hed, Lisa
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Sande, Olow
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Åhag, Per
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Studenternas förkunskaper2020Ingår i: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, Vol. 46, nr 4, s. 25-31Artikel i tidskrift (Refereegranskat)
  • 4.
    Åhag, Per
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    The complex Monge-Ampére operator on bounded hyperconvex domains2002Doktorsavhandling, monografi (Övrigt vetenskapligt)
  • 5.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cegrell, Urban
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyz, Rafal
    Jagiellonian University, Krakow, Poland.
    On Dirichlet's principle and problem2012Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 110, nr 2, s. 235-250Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The aim of this paper is to give a new proof of the complete characterization of measures for which there exists a solution of the Dirichlet problem for the complex Monge-Ampere operator in the set of plurisubharmonic functions with finite pluricomplex energy. The proof uses variational methods.

  • 6.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cegrell, Urban
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyz, Rafal
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Vector spaces of delta-plurisubharmonic functions and extensions of the complex Monge-Ampere operator2015Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 422, nr 2, s. 960-980Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we shall consider two types of vector ordering on the vector space of differences of negative plurisubharmonic functions, and the problem whether it is possible to construct supremum and infimum. Then we consider two different approaches to define the complex Monge-Ampere operator on these vector spaces, and we solve some Dirichlet problems. We end this paper by stating and discussing some open problems.

  • 7.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cegrell, Urban
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyz, Rafal
    Phạm, Hoàng Hiệp
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Monge-Ampère measures on pluripolar sets2009Ingår i: Journal des Mathématiques Pures et Appliquées, ISSN 0021-7824, E-ISSN 1776-3371, Vol. 92, nr 6, s. 613-627Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this article we solve the complex Monge–Ampère problem for measures with large singular part. This result generalizes classical results by Demailly, Lelong and Lempert a.o., who considered singular parts carried on discrete sets. By using our result we obtain a generalization of Kołodziej's subsolution theorem. More precisely, we prove that if a non-negative Borel measure is dominated by a complex Monge–Ampère measure, then it is a complex Monge–Ampère measure.

  • 8.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cegrell, Urban
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Hiep, Pham Hoang
    On the Guedj-Rashkovskii conjecture2019Ingår i: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 123, nr 1, s. 15-20Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove some cases when the Guedj-Rashkovskii conjecture holds.

  • 9.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cegrell, Urban
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Kolodziej, Slawomir
    Phạm, Hoàng Hiệp
    Zeriahi, Ahmed
    Partial pluricomplex energy and integrability exponents of plurisubharmonic functions2009Ingår i: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 222, nr 6, s. 2036-2058Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We first prove a quantitative estimate of the volume of the sublevel sets of a plurisubharmonic function in a hyperconvex domain with boundary values 0 (in a quite general sense) in terms of its Monge–Ampère mass in the domain. Then we deduce a sharp sufficient condition on the Monge–Ampère mass of such a plurisubharmonic function φ for exp(−2φ) to be globally integrable as well as locally integrable.

  • 10. Åhag, Per
    et al.
    Cegrell, Urban
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Pham, Hoang Hiep
    A product property for the pluricomplex energy2010Ingår i: Osaka Journal of Mathematics, ISSN 0030-6126, Vol. 47, nr 3, s. 637-650Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this note we prove a product property for the pluricomplex energy, and then give some applications.

  • 11.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Cegrell, Urban
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Phạm, Hoàng Hiệp
    Monge-Ampère measures on subvarieties2015Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 423, s. 94-105Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this article we address the question whether the complex Monge-Ampere equation is solvable for measures with large singular part. We prove that under some conditions there is no solution when the right-hand side is carried by a smooth subvariety in C-n of dimension k < n.

  • 12.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyz, Rafal
    Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland.
    An inequality for the beta function with application in pluripotential theory2009Ingår i: Journal of inequalities and applications, ISSN 1025-5834, E-ISSN 1029-242X, s. 901397-8 pagesArtikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove in this paper an inequality for the beta function, and we give an application in pluripotential theory.

  • 13.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyz, Rafal
    Kolodziej's subsolution theorem for unbounded pseudoconvex domains2012Ingår i: Universitatis Iagellonicae Acta Mathematica, ISSN 0083-4386, 2084-3828, Vol. 50, s. 7-23Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we generalize Kolodziej's subsolution theorem to bounded and unbounded pseudoconvex domains, and in that way we are able to solve complex Monge-Ampère equations on general pseudoconvex domains. We then give a negative answer to a question of Cegrell and Kolodziej by constructing a compactly supported Radon measure µ that vanishes on all pluripolar sets in Cn such that µ(Cn) = (2π)n, and forwhich there is no function u in L+ such that (ddcu)=µ. We end this paper by solving a Monge-Ampère type equation. Furthermore, we proveuniqueness and stability of the solution.

  • 14.
    Åhag, Per
    et al.
    Department of Natural Sciences, Engineering and Mathematics, Mid Sweden University, SE-871 88 Härnösand, Sweden.
    Czyz, Rafal
    Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland.
    Modulability and duality of certain cones in pluripotential theory2010Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 361, nr 2, s. 302-321Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let p>0, and let Ep denote the cone of negative plurisubharmonic functions with finite pluricomplex p-energy. We prove that the vector space δEp=EpEp, with the vector ordering induced by the cone Ep is σ-Dedekind complete, and equipped with a suitable quasi-norm it is a non-separable quasi-Banach space with a decomposition property with control of the quasi-norm. Furthermore, we explicitly characterize its topological dual. The cone Ep in the quasi-normed space δEp is closed, generating, and has empty interior.

  • 15.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyz, Rafal
    On a characterization of m-subharmonic functions with weak singularities2019Ingår i: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 123, nr 1, s. 21-29Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We provide a characterization of functions in Cegrell’s energy class Ep,m.

  • 16.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyz, Rafal
    On the Blocki-Zwonek conjectures2015Ingår i: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 60, nr 9, s. 1270-1276Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let Omega be a bounded pseudoconvex domain in C-n, and let g(Omega) (z, a) be the pluricomplex Green function with pole at a in Omega. It was conjectured by Blocki and Zwonek that the function given by beta = beta(Omega),(a) : (-infinity, 0) (sic) t -> beta(t) = log (lambda(n)({z is an element of Omega g(Omega) (z, a) < t})) is convex. Here.n is the Lebesgue measure in Cn. In this note we give an affirmative answer to this conjecture when Omega is biholomorphic to the unit ball or to the polydisc in C-n, n >= 1.

  • 17.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyz, Rafal
    Poincare- and Sobolev- Type Inequalities for Complex m-Hessian Equations2020Ingår i: Results in Mathematics, ISSN 1422-6383, Vol. 75, nr 2, artikel-id 63Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    By using quasi-Banach techniques as key ingredient we prove Poincaré- and Sobolev- type inequalities for m-subharmonic functions with finite (pm)-energy. A consequence of the Sobolev type inequality is a partial confirmation of Błocki’s integrability conjecture for m-subharmonic functions.

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  • 18.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyz, Rafal
    Hed, Lisa
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    The Dirichlet problem for m-subharmonic functions on compact sets2020Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 126, nr 3, s. 497-512Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We characterize those compact sets for which the Dirichlet problem has a solution within the class of continuous m-subharmonic functions defined on a compact set, and then within the class of m-harmonic functions.

  • 19.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyz, Rafal
    Hed, Lisa
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    The Geometry of m-Hyperconvex Domains2018Ingår i: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 28, nr 4, s. 3196-3222Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the geometry of m-regular domains within the Caffarelli–Nirenberg–Spruck model in terms of barrier functions, envelopes, exhaustion functions, and Jensen measures. We prove among other things that every m-hyperconvex domain admits an exhaustion function that is negative, smooth, strictly m-subharmonic, and has bounded m-Hessian measure.

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  • 20.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyz, Rafal
    Lundow, Per-Håkan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    A counterexample to a conjecture by Blocki-Zwonek2018Ingår i: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 27, nr 1, s. 119-124Artikel i tidskrift (Refereegranskat)
  • 21.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyz, Rafal
    Persson, Leif
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Radially symmetric plurisubharmonic functions2012Ingår i: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 106, s. 1-17Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this note we consider radially symmetric plurisubharmonic functions and the complex Monge–Ampère operator. We prove among other things a complete characterization of unitary invariant measures for which there exists a solution of the complex Monge–Ampère equation in the set of radially symmetric plurisubharmonic functions. Furthermore, we prove in contrast to the general case that the complex Monge–Ampère operator is continuous on the set of radially symmetric plurisubharmonic functions. Finally we characterize radially symmetric plurisubharmonic functions among the subharmonic ones using merely the laplacian.

  • 22.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyz, Rafał
    Jagiellonian University, Faculty of Mathematics and Computer Science, Kraków, Poland.
    On the complex Monge-Ampère operator in unbounded domains2017Ingår i: Universitatis Iagellonicae Acta Mathematica, ISSN 0860-0120, Vol. 54, s. 7-13Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this note we give sufficient conditions on a measure μ defined on a unbounded strictly hyperconvex domain in ℂn, to be the Monge-Ampère measure of some plurisubharmonic function. These generalize recent results by Lê et al.

  • 23.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyż, R.
    Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, Kraków, Poland.
    Lundow, Per-Håkan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On a generalised Lambert W branch transition function arising from p,q-binomial coefficients2024Ingår i: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 462, artikel-id 128347Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    With only a complete solution in dimension one and partially solved in dimension two, the Lenz-Ising model of magnetism is one of the most studied models in theoretical physics. An approach to solving this model in the high-dimensional case (d>4) is by modelling the magnetisation distribution with p,q-binomial coefficients. The connection between the parameters p,q and the distribution peaks is obtained with a transition function ω which generalises the mapping of Lambert W function branches W0 and W−1 to each other. We give explicit formulas for the branches for special cases. Furthermore, we find derivatives, integrals, parametrizations, series expansions, and asymptotic behaviours.

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  • 24.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyż, Rafał
    Institute of Mathematics Jagiellonian University, Lojasiewicza 6, Kraków, Poland.
    A characterization of the degenerate complex Hessian equations for functions with bounded (p, m)-energy2023Ingår i: Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, ISSN 0391-173X, E-ISSN 2036-2145, Vol. 24, nr 3, s. 1853-1873Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    By proving an estimate of the sublevel sets for (ω, m)-subharmonic functions, we obtain a Sobolev-type inequality that is then used to characterize the degenerate complex Hessian equations for functions with bounded (p, m)-energy defined on compact Kähler manifolds. This paper is a continuation of the work of Lu and Nguyen.

  • 25.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyż, Rafał
    Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland.
    Geodesics in the space of m-subharmonic functions with bounded energy2023Ingår i: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, Vol. 2023, nr 12, s. 10115-10155Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We raise our cups to Urban Cegrell, gone but not forgotten, gone but ever here. Until we meet again in Valhalla!

    With inspiration from the Kähler geometry, we introduce a metric structure on the energy class, E1,m, of m-subharmonic functions with bounded energy and show that it is complete. After studying how the metric convergence relates to the accepted convergences in this Caffarelli–Nirenberg–Spruck model, we end by constructing geodesics in a subspace of our complete metric space.

  • 26.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyż, Rafał
    Institute of Mathematics Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland.
    On a family of quasimetric spaces in generalized potential theory2022Ingår i: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 32, nr 4, artikel-id 117Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We construct a family of quasimetric spaces in generalized potential theory containing m-subharmonic functions with finite (pm)-energy. These quasimetric spaces will be viewed both in Cn and in compact Kähler manifolds, and their convergence will be used to improve known stability results for the complex Hessian equations.

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  • 27.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyż, Rafał
    On the Blocki-Zwonek conjectures and beyond2015Ingår i: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 105, nr 4, s. 371-380Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let \({\Omega}\) be a bounded pseudoconvex domain in \({\mathbb{C}^n}\), and let \({g_{\Omega}(z,a)}\) be the pluricomplex Green function with pole at a in \({\Omega}\). Błocki and Zwonek conjectured that the function given by $$\begin{array}{ll}\alpha = \alpha_{\Omega}, a: (- \infty, 0) \ni t \mapsto \alpha (t) = e^{-2nt} \lambda_n \left( \{z \in \Omega: g_{\Omega}(z, a) < t \} \right)\end{array}$$ is nondecreasing, and that the function given by $$\begin{array}{ll}\beta = \beta_{\Omega}, a: (-\infty, 0) \ni t \to \beta(t)= \log \left(\lambda_n \left(\{z \in \Omega: g_{\Omega}(z,a)< t\}\right)\right)\end{array}$$ is convex. Here \({\lambda_{n}}\) is the Lebesgue measure in \({\mathbb{C}^n}\). In this note we give an affirmative answer to these conjectures when \({\Omega}\) is biholomorphic to a bounded, balanced, and pseudoconvex domain in \({\mathbb{C}^n}\), \({n\geq 1}\). The aim of this note is to consider generalizations of the functions \({\alpha}\), \({\beta}\) defined by the Green function with two poles in \({\mathbb{D}\subset\mathbb{C}}\). We prove that \({\alpha}\) is not nondecreasing, and \({\beta}\) is not convex. By using the product property for pluricomplex Green functions, we then generalize this to n-dimensions. Finally, we end this note by considering two other possibilities generalizing the Błocki–Zwonek conjectures.

  • 28.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyż, Rafał
    On the Moser-Trudinger inequality in complex space2019Ingår i: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 479, nr 2, s. 1456-1474Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we prove the pluricomplex counterpart of the Moser-Trudinger and Sobolev inequalities in complex space. We consider these inequalities for plurisubharmonic functions with finite pluricomplex energy, and we estimate the concerned constants.

  • 29.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyż, Rafał
    Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, Kraków, Poland.
    On the regularity of the complex hessian equation2022Ingår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 150, nr 12, s. 5311-5320Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This note aims to investigate the regularity of a solution to the Dirichlet problem for the complex Hessian equation, which has a density of the m-Hessian measure that belongs to Lq, for q ≤ mn.

  • 30.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyż, Rafał
    Hed, Lisa
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Extension and approximation of m-subharmonic functions2018Ingår i: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 63, nr 6, s. 783-801Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Let  be a bounded domain, and let f be a real-valued function defined on the whole topological boundary . The aim of this paper is to find a characterization of the functions f which can be extended to the inside to a m-subharmonic function under suitable assumptions on . We shall do so using a function algebraic approach with focus on m-subharmonic functions defined on compact sets. We end this note with some remarks on approximation of m-subharmonic functions.

  • 31.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Czyż, Rafał
    Hed, Lisa
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    The classification of holomorphic (m, n)-subharmonic morphisms2020Ingår i: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 65, nr 2, s. 152-177Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study the problem of classifying the holomorphic (m, n)-subharmonic morphisms in complex space. This determines which holomorphic mappings preserves m-subharmonicity in the sense that the composition of the holomorphic mapping with a m-subharmonic functions is n-subharmonic. We show that there are three different scenarios depending on the underlying dimensions, and the model itself. Either the holomorphic mappings are just the constant functions, or up to composition with a homotethetic map, canonical orthogonal projections. Finally, there is a more intriguing case when subharmonicity is gained.

  • 32.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Hed, Lisa
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Leijon, R.
    Clear Street Markets LLC, NY, New York, United States.
    Nordenfors, Oskar
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Olsson, L.
    Mid Sweden University, Department of Communication, Quality Management and Information Systems, Sundsvall, Sweden.
    Industrial engineering and management students envision AI's role in the industry2023Ingår i: 2023 IEEE International Conference on Industrial Engineering and Engineering Management, IEEE, 2023, s. 903-907Konferensbidrag (Refereegranskat)
    Abstract [en]

    This study explores the perceptions of master's program students in Industrial Engineering and Management (IEM) at Umeå University, Sweden, concerning the current and future impact of artificial intelligence (AI) on their discipline. Employing a descriptive, cross-sectional survey design, we collected quantitative data from participants asked to assess AI's influence on decision-making, human-computer interactions, and information management, among other areas. While ordinal regression analysis revealed no significant correlation between the student's academic year and their survey responses, a Wilcoxon signed-rank test indicated a statistically significant belief that AI's impact on all surveyed areas would intensify within the next decade. Our findings suggest a need for engineering education to evolve to adequately equip future professionals for the expanding influence of AI in IEM. Furthermore, the results add to the ongoing discussion of AI's role in engineering education and the broader industrial engineering and management field.

  • 33.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Hed, Lisa
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Lundow, Per-Håkan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Olsson, Leif
    Department of Information Systems and Technology, Mid Sweden University, Sundsvall, Sweden.
    Are we ready for agenda 2030 for Sustainable Development?2019Ingår i: 2019 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), IEEE, 2019, s. 224-227Konferensbidrag (Refereegranskat)
    Abstract [en]

    Are we as educators of future engineers ready for the United Nations Agenda 2030 for sustainable development? We make a comparative study of the Master's programme in Industrial Engineering and Management at two Swedish Universities. Our conclusion is that we as educators and programme managers are not yet in the right process for Agenda 2030 and the necessary transition into a sustainable future.

  • 34.
    Åhag, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Hsu, Y.J.
    Nanyang Technological University, Asian School of the Environment, Singapore, Singapore.
    Olsson, L.
    Mid Sweden University, Department of Information Systems and Technology, Sundsvall, Sweden.
    Sundberg, L.
    Mid Sweden University, Department of Information Systems and Technology, Sundsvall, Sweden.
    The impact of SARS-CoV-2 on engineering education: Student perceptions from three countries2020Ingår i: 2020 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), IEEE, 2020, s. 1266-1270, artikel-id 9309900Konferensbidrag (Refereegranskat)
    Abstract [en]

    The outbreak and rapid spread of SARS-CoV-2, commonly known as COVID-19, has led to a loss of life, widely spread economic consequences, and changed behavior in many, if not all, sectors of society. One such sector is institutes for higher education. Against this backdrop, in this paper, we aim to study how engineering training was affected at the beginning of this global pandemic. The point of departure in the paper is the students' perceptions. Our study is based on survey responses from students from Singapore, Sweden and Taiwan. Three themes were identified in the results: a) issues related to transitioning from the physical classroom to an online environment, b) examination activities, and c) perceptions about the future. As such, this paper contributes with first-hand experiences and reflections on engineering training during a global crisis.

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