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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Nonradial Hörmander algebras of several variables and convolution operators
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by José Bonet, Antonio Galbis and Siegfried Momm PDF
Trans. Amer. Math. Soc. 353 (2001), 2275-2291 Request permission

Abstract:

A characterization of the closed principal ideals in nonradial Hörmander algebras of holomorphic functions of several variables in terms of the behaviour of the generator is obtained. This result is applied to study the range of convolution operators and ultradifferential operators on spaces of quasianalytic functions of Beurling type. Contrary to what is known to happen in the case of non-quasianalytic functions, an ultradistribution on a space of quasianalytic functions is constructed such that the range of the operator does not contain the real analytic functions.
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Additional Information
  • José Bonet
  • Affiliation: Departamento de Matemática Aplicada, E.T.S. Arquitectura, E-46071 Valencia, Spain
  • ORCID: 0000-0002-9096-6380
  • Email: jbonet@mat.upv.es
  • Antonio Galbis
  • Affiliation: Departamento de Análisis Matemático, Universidad de Valencia, E-46100 Burjasot (Valencia), Spain
  • Email: Antonio.Galbis@uv.es
  • Siegfried Momm
  • Affiliation: Mathematisches Institut, Heinrich-Heine-Universität, D-40225 Düsseldorf 1, Germany
  • Email: momm@mx.cs.uni-duesseldorf.de, siegfried.momm@t-online.de
  • Received by editor(s): June 1, 1998
  • Published electronically: February 7, 2001
  • Additional Notes: The research of J.Bonet and A.Galbis was supported in part by DGESIC, Proyecto no. PB97-0333.

    • Dedicated: To our friend Jean Schmets on the occasion of his 60th birthday
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 2275-2291
  • MSC (2000): Primary 46E10, 46F05, 46F10, 35R50, 32A15
  • DOI: https://doi.org/10.1090/S0002-9947-01-02780-5
  • MathSciNet review: 1814070