Geodesic
Generalized Dirichlet classes in a~half-plane and their application to approximations
Sbornik. Mathematics, Tome 206 (2015) no. 1, pp. 135-160

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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, generalized Bergman and Dirichlet classes, zero set, completeness of a system of exponentials.
Mots-clés : Laplace transform 
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A. M. Sedletskii. Generalized Dirichlet classes in a~half-plane and their application to approximations. Sbornik. Mathematics, Tome 206 (2015) no. 1, pp. 135-160. http://geodesic.mathdoc.fr/item/SM_2015_206_1_a8/