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Sbornik: Mathematics, 2015, Volume 206, Issue 1, Pages 135–160
DOI: https://doi.org/10.1070/SM2015v206n01ABEH004450
(Mi sm8396)
 

Generalized Dirichlet classes in a half-plane and their application to approximations

A. M. Sedletskii

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: We introduce generalized Dirichlet classes of analytic functions in a disc and a half-plane. We establish a relationship between these classes and their zero sets. A precise sufficient condition for a zero subset of a generalized Dirichlet class in a half-plane is obtained. Using this condition, we prove a necessary condition (which is also precise) for a system of exponential functions to be complete in the space $L^2$ on a half-line with regularly varying weight of order $\alpha\in[-1,0]$.
Bibliography: 18 titles.
Keywords: slowly varying function, Laplace transform, generalized Bergman and Dirichlet classes, zero set, completeness of a system of exponentials.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00281
This work was supported by the Russian Foundation for Basic Research (grant no. 13-01-00281).
Received: 25.06.2014 and 14.10.2014
Bibliographic databases:
Document Type: Article
UDC: 517.547.5+517.518.32
MSC: Primary 42A65; Secondary 32A60
Language: English
Original paper language: Russian
Citation: A. M. Sedletskii, “Generalized Dirichlet classes in a half-plane and their application to approximations”, Sb. Math., 206:1 (2015), 135–160
Citation in format AMSBIB
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\paper Generalized Dirichlet classes in a~half-plane and their application to approximations
\jour Sb. Math.
\yr 2015
\vol 206
\issue 1
\pages 135--160
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  • https://doi.org/10.1070/SM2015v206n01ABEH004450
  • https://www.mathnet.ru/eng/sm/v206/i1/p147
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