Nonradial Hörmander algebras of several variables and convolution operators-Reference-Cited by-同舟云学术

Nonradial Hörmander algebras of several variables and convolution operators

Published:2001-02-07 Issue:6 Volume:353 Page:2275-2291
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Bonet José,Galbis Antonio,Momm Siegfried

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/2001-353-06/S0002-9947-01-02780-5/S0002-9947-01-02780-5.pdf

Reference32 articles.

1. Asymptotic behavior of subharmonic functions of finite order;Azarin, V. S.;Mat. Sb. (N.S.),1979

2. Interpolation problems in 𝐶ⁿ with applications to harmonic analysis;Berenstein, C. A.;J. Analyse Math.,1980

3. On some problems concerning subordination and majorization of functions;Szynal, Anna;Demonstratio Math.,1978

4. Modular estimates for linear integral operators in Musielak-Orlicz spaces on groups;Bardaro, Carlo;Atti Sem. Mat. Fis. Univ. Modena,1995

5. On the range of convolution operators on non-quasianalytic ultradifferentiable functions;Bonet, J.;Studia Math.,1997

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