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Mat. Sb., 2015, Volume 206, Number 1, Pages 147–174 (Mi msb8396)  

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

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).


DOI: https://doi.org/10.4213/sm8396

Full text: PDF file (636 kB)
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English version:
Sbornik: Mathematics, 2015, 206:1, 135–160

Bibliographic databases:

UDC: 517.547.5+517.518.32
MSC: Primary 42A65; Secondary 32A60
Received: 25.06.2014 and 14.10.2014

Citation: A. M. Sedletskii, “Generalized Dirichlet classes in a half-plane and their application to approximations”, Mat. Sb., 206:1 (2015), 147–174; Sb. Math., 206:1 (2015), 135–160

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