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Abstract <p>In this survey, we present recent results of Paley–Wiener type for new weighted spaces of analytic functions on the unit disc and upper half-plane, defined in terms of the Fourier transform. These spaces are generalizations of classical weighted spaces of analytic functions of Bergman–Djrbashian type. Theorems of Paley–Wiener type, in fact, provide possibilities for further study of these new spaces and classical Toeplitz type operators and algebras of such operators in these spaces.</p>

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Paley–Wiener Type Theorems for Spaces of Analytic Functions with Mixed Fourier Norm

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • A. N. Karapetyants,
  • I. Yu. Smirnova

摘要

Abstract

In this survey, we present recent results of Paley–Wiener type for new weighted spaces of analytic functions on the unit disc and upper half-plane, defined in terms of the Fourier transform. These spaces are generalizations of classical weighted spaces of analytic functions of Bergman–Djrbashian type. Theorems of Paley–Wiener type, in fact, provide possibilities for further study of these new spaces and classical Toeplitz type operators and algebras of such operators in these spaces.