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Beurling's analyticity theorem for quantum differences
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
2008 (English)In: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 127, no 3, 369-380 p.Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Berlin: Springer-Verlag , 2008. Vol. 127, no 3, 369-380 p.
Keyword [en]
quantum difference, quantum analysis, analyticity
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-10136DOI: 10.1007/s00229-008-0213-8OAI: oai:DiVA.org:umu-10136DiVA: diva2:149807
Available from: 2010-01-25 Created: 2008-06-19 Last updated: 2017-12-14Bibliographically approved

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