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  • 1.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    A generalization of a theorem of G. Freud on the differentiability of functions1985Inngår i: Acta Scientarum Mathematicarum, ISSN 0001-6969, Vol. 49, nr 1-4, s. 271-281Artikkel i tidsskrift (Fagfellevurdert)
  • 2.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    A note on capacity and Hausdorff measure in homogeneous spaces1997Inngår i: Potential analysis, Vol. 6Artikkel i tidsskrift (Fagfellevurdert)
  • 3.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    A note on Gram-Schmidt's algorithm for a general angle2009Inngår i: Normat, ISSN 0801-3500, Vol. 57, nr 4, s. 173-179Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [sv]

    Gram-Schmidts algoritm ger en parvis ortogonal mängd från en linjärt oberoende mängd i ett allmännt vektorrum med inre produkt. Vi ger en algoritm som konstruerar en mängd där vektorerna parvis har en godtycklig på förhand given vinkel, i alla fall där detta är möjligt.

  • 4.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    A note on the Carleman condition for determinacy of moment problems1987Inngår i: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 25, nr 2, s. 289-294Artikkel i tidsskrift (Fagfellevurdert)
  • 5.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    A note on the harmonic derivative2004Inngår i: Real Analysis Exchange, ISSN 0147-1937, Vol. 30, s. 11-21Artikkel i tidsskrift (Fagfellevurdert)
  • 6.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Bernstein's analyticity theorem for binary differences1999Inngår i: Mathematische Annalen, ISSN 0025-5831 (paper), 1432-1807 (e), Vol. 315, nr 2, s. 251-261Artikkel i tidsskrift (Fagfellevurdert)
  • 7.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Bernstein's analyticity theorem for quantum differences2007Inngår i: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 57, nr 1, s. 67-73Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider real valued functions f defined on a subinterval I of the positive real axis and prove that if all of f's quantum differences are nonnegative then f has a power series representation on I. Further, if the quantum differences have fixed sign on I then f is analytic on I.

  • 8.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Bessel potentials and extension of continuous functione on compact sets1975Inngår i: Arkiv för matematik, ISSN 0004-2080 (p), 1871-2487 (e), Vol. 13, nr 2, s. 263-271Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We characterize the compact sets K in the n-dimensional Euclidean space with capacity zero relative to a certain kernel as exactly those sets for which every continous function on K has an extension to a continuous potential in the full space. A special case in the Bessel kernel and the related capacity.

  • 9.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Beurling's analyticity theorem for quantum differences2008Inngår i: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 127, nr 3, s. 369-380Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A theorem of Beurling states that if f satisfies , n = 1, 2,..., for some 0 < ρ < 2, on a real interval I, then f is analytic in a rhombus containing I. We study the corresponding problem for the quantum differences Δ n f (q, x), q > 1, n = 1, 2,..., for functions defined on (0, ∞) and prove quantitative and qualitative analogues of Beurling’s result. We also characterize the analyticity of f on subintervals of (0, ∞) in q-analytic terms.

  • 10.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Capacities of compact sets in linear subspaces of R^n1978Inngår i: Pacific Journal of Mathematics, ISSN 0030-8730, Vol. 78, nr 1, s. 261-266Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We characterize the exceptional sets for Besov spaces in the n-dimensional Euclidean space by an extension property for continuous functions and prove an inequality between Bessel and Besov capacities.

  • 11.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Continuous functions and Riesz type potentials in homogeneous spaces2015Inngår i: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 43, nr 3, s. 495-511Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We develop a potential theory for a Riesz type kernel in a homogeneous space and characterize the compact sets K with capacity zero as the sets K for which every continous function f on K is the restriction to K of a continuous potential Uσfk of an absolutely continuous measure σ f supported in an arbitrarily small neighbourhood of K. The measure σ f can be choosen as a suitable restriction of a single measure σ that only depends on the set K and the kernel k.

  • 12.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Explaining Kummer's test2015Manuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    Mathematical theorems and their proofs are often described as being beautyful, natural or explanatory. This paper treats the last case  and discusses explanatory versus non explanatory proofs using  a convergence theorem for positive series due to Kummer, called Kummer's test. This example was studied by Pringsheim already in the beginning in the last century and has recently been discussed by Hafner and Mancuso in relation to Steiner's criteria for an explanatory proof. We provide a mathematical analysis of Kummer's test and give a proof that we claim is explanatory in this sense. Besides this we answer a number of questions that are frequently asked about the test.

  • 13.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Local and global weighted norm inequalities for thr sharp function and the Hardy-Littlewood maximal function1993Inngår i: Ricerche di Matamatica, Vol. 42, nr 2Artikkel i tidsskrift (Fagfellevurdert)
  • 14.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Nonlinear potential theory in Lebesque spaces with mixed norm1988Inngår i: Potential Theory, Prague, 1987 / [ed] J. Kral, J. Lukes, I. Netuka, J. Vesely, New York: Plenum Publishing Corporation , 1988, s. 325-331Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The classical potential theory for the Riesz kernel in the d-dimentional Euclidean space has been generalized in many different ways. We are here concerned with the L^p-potential theory which appeared around 1970 in papers by V.G. Maz'ya, V. P, Havin and N. G. Mayers. In this paper we extend that theory to the so called Lebesgue spaces with mixed norm.

  • 15.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    On Lp-differentiability and difference properties of functions1982Inngår i: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 74, nr 2, s. 153-168Artikkel i tidsskrift (Fagfellevurdert)
  • 16.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On Mixtures of Gamma Distributions, Distributions with Hyperbolically Monotone Densities and Generalized Gamma Convolutions (GGC)2019Inngår i: Probability and Mathematical Statistics, ISSN 0208-4147Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let Y be a standard Gamma(k) distributed random variable (rv), k > 0, and let X be an independent positive rv. If X has a hyperbolically monotone density of order k (HMk), then Y ·X and Y/X are generalized gamma convolutions (GGC). This extends work by Roynette et al. and Behme and Bondesson. The same conclusion holds with Y replaced by a finite sum of independent gamma variables with sum of shape parameters at most k. Both results are applied to subclasses of GGC.

  • 17.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On Multivariate Hyperbolically Completely Monotone Densities and Their Laplace transforms2015Manuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    We study classes of multivariate (bivariate) random variables with hyperbolically completely monotone densities (MVHCM) and prove that these classes are closed with respect to the Laplace transform. We then use this result to define new classes of bivariate generalized gamma convolutions (BVGGC_L) that contain Bondesson's class BVGGC in the strong sense.

  • 18.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    On ordinary differentiability of Bessel potentials1984Inngår i: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 44, nr 3, s. 325-352Artikkel i tidsskrift (Fagfellevurdert)
  • 19.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    On properties of functions with conditions on their mean oscillation over cubes1982Inngår i: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 20, nr 2, s. 275-291Artikkel i tidsskrift (Fagfellevurdert)
  • 20.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    On s-sets and mutual absolute continuity of measures on homogeneous spaces1997Inngår i: Manuscripta Mathematica, ISSN 0025-2611 (p), 1432-1785 (e), Vol. 94, s. 169-186Artikkel i tidsskrift (Fagfellevurdert)
  • 21.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    On the almost everywhere differentiability of the metric projection on closed sets in lp(ℝn), 2 < p < ∞2018Inngår i: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 68, nr 143, s. 943-951Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Let F be a closed subset of ℝn and let P(x) denote the metric projection (closest point mapping) of x ∈ ℝn onto F in lp-norm. A classical result of Asplund states that P is (Fréchet) differentiable almost everywhere (a.e.) in ℝn in the Euclidean case p = 2. We consider the case 2 < p < ∞ and prove that the ith component Pi(x) of P(x) is differentiable a.e. if Pi(x) 6= xi and satisfies Hölder condition of order 1/(p−1) if Pi(x) = xi.

  • 22.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Polar sets and capacitary potentials in homogeneous spaces2013Inngår i: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 38, s. 771-783Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A set E in a space X is called a polar set in X, relative to a kernel k(x; y), if thereis a nonnegative measure in X such that the potential Uk(x) = ∞ precisely when x ∈ E. Polarsets have been characterized in various classical cases as G-sets (countable intersections of opensets) with capacity zero. We characterize polar sets in a homogeneous space (X; d; ) for severalclasses of kernels k(x; y), among them the Riesz -kernels and logarithmic Riesz kernels. The latercase seems to be new even in Rn.

  • 23.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    The fundamental theorem of algebra2014Inngår i: Proofs from THE BOOK / [ed] Martin Aigner, Günter M. Ziegler, Berlin-Heidelberg: Springer, 2014, 5, s. 147-149Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    Everyn nonconstant polynomial with complex coefficients has at least one root in the field of complex numbers

  • 24.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Thinness in non-linear potential theory for non-isotropic Sobolev spaces1997Inngår i: Ann. Acad. Aci. Fenn., Vol. 22Artikkel i tidsskrift (Fagfellevurdert)
  • 25.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Weighted Lp-inequalities for multi-parameter Riesz type potentials and strong fractional maximal operators2007Inngår i: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 337, s. 317-333Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove weighted L^p-inequalities  for multi-parameter Riesz type potentials, strong fractional maximal operators and their dyadic counterparts. Our proofs avoids the Good-Lambda inequalities used earlier in the R^m-case and are based on our integrated multi-parameter summation by parts lemma, that might be of independent interest.

  • 26.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Weighted norm inequalities for Riesz potentials and fractional maximal functions in mixed norm Lebesgue spaces1990Inngår i: Studia Mathematica, ISSN 0039-3233, Vol. 97, nr 3, s. 239-244Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Norm inequalities for Riesz potentials and fractional maximal functions in weighted Lebesgue spaces were proved by Muckenhoupt and Wheeden in the 1970's. We prove such inequalities in weighted mixed norm Lebesgue spaces for the full range oh indices. Our proofs make extensive use of the concept of independence of weights in the Muckenhoupt classes.

  • 27.
    Sjödin, Tord
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
    Wolff's inequality in multi-parameter Morrey spaces2012Inngår i: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 271, nr 3, s. 781-787Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We prove Wolff inequalities for multi-parameter Riesz potentials and Wolff potentials in Lebesque spaces Lp(Rd) and multi-parameter Morrey spaces Lp λ(Rd), where Rd = Rn1 × Rn2 ×···× Rnk , λ = (λ1,...,λk) and 0 < λi ≤ ni, 1 ≤ i ≤ k, in the dyadic case as well as in the non-dyadic (continuous) case.

  • 28.
    Sjödin, Tord
    et al.
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Matematik och matematisk statistik.
    Løvtrup, Søren
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Biologi, miljö- och geovetenskap.
    Biomathematics and the fate map of the amphibian blastula1990Inngår i: Rivista di Biologia - Biology forum, ISSN 0035-6050, Vol. 83, nr 1, s. 81-92Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A fate map of the amphibian embryo has been drawn by a computer on the basis of two simple and well-known processes of the cell differentiation. The two processes are related in so far as they both consist of the formation of a new type of cells, here called f-cells. The first process is the spontaneous formation of the Ruffini cells along the marginal edge around the circumference of the embryo, slightly below the equator. When this occurs, they will induce the neighbouring cells located towards the animal pole to undergo the same differentiation, and the induction, which seems to be rather an activation, spreads from cell to cell. The actual shape of the map is due to the fact that the formation of the Ruffine cells occurs along a temporal gradient from the dorsal to the ventral side.

1 - 28 of 28
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