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Nonradial Hörmander algebras of several variables and convolution operators


Authors: José Bonet, Antonio Galbis and Siegfried Momm
Journal: Trans. Amer. Math. Soc. 353 (2001), 2275-2291
MSC (2000): Primary 46E10, 46F05, 46F10, 35R50, 32A15
Published electronically: February 7, 2001
MathSciNet review: 1814070
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Abstract | References | Similar Articles | Additional Information

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
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

DOI: https://doi.org/10.1090/S0002-9947-01-02780-5
Keywords: H\"ormander algebras, principal ideal, convolution operators, spaces of quasianalytic functions, real analytic functions
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
Article copyright: © Copyright 2001 American Mathematical Society