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Theorems of Paley–Wiener Type for Spaces of Polyanalytic Functions

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Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

Abstract

We prove Paley–Wiener theorems for the true poly-Bergman and poly-Bergman spaces based on properties of the compression of the Beurling–Ahlfors transform to the upper half-plane. An isometric isomorphism between j copies of the Hardy space and the poly-Bergman space of order j is constructed.

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Author information

Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049 001, Lisboa, Portugal

    Luís V. Pessoa & Ana Moura Santos

Authors
  1. Luís V. Pessoa
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  2. Ana Moura Santos
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Corresponding author

Correspondence to Luís V. Pessoa .

Editor information

Editors and Affiliations

  1. Dept. of Computer Sc. & Comp. Methods, Pedagogical University, Kraków, Poland

    Vladimir V. Mityushev

  2. Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

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Pessoa, L.V., Santos, A.M. (2015). Theorems of Paley–Wiener Type for Spaces of Polyanalytic Functions. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_66

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