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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Perturbations of surjective convolution operators


Authors: C. Fernández, A. Galbis and D. Jornet
Journal: Proc. Amer. Math. Soc. 130 (2002), 2377-2381
MSC (2000): Primary 46F05; Secondary 46F10.
Published electronically: February 12, 2002
MathSciNet review: 1897463
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Abstract: Let $\mu_1$ and $\mu_2$ be (ultra)distributions with compact support which have disjoint singular supports. We assume that the convolution operator $f\, \rightarrow \, \mu_1 * f$ is surjective when it acts on a space of functions or (ultra)distribu- tions, and we investigate whether the perturbed convolution operator $f\rightarrow$ $(\mu_1 + \mu_2)* f$ is surjective. In particular we solve in the negative a question asked by Abramczuk in 1984.


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Additional Information

C. Fernández
Affiliation: Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, E-46100 Burjassot (Valencia), Spain
Email: Carmen.Fdez-Rosell@uv.es

A. Galbis
Affiliation: Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, E-46100 Burjassot (Valencia), Spain
Email: Antonio.Galbis@uv.es

D. Jornet
Affiliation: Departamento de Matemática Aplicada, E.T.S. Arquitectura, Universidad Politéc- nica de Valencia, Camino de Vera, E-46071 Valencia, Spain
Email: dajorca@mat.upv.es

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06359-1
PII: S 0002-9939(02)06359-1
Keywords: Convolution operator, slowly decreasing, ultradistributions.
Received by editor(s): July 24, 2000
Received by editor(s) in revised form: March 22, 2001
Published electronically: February 12, 2002
Additional Notes: This work was completed with the support of DGESIC under Proyecto PB97-0333.
The third author was also supported by Ministerio de Educación y Cultura, grant FP98 48285420.
The authors want to express their gratitude to the referee for helpful suggestions.
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2002 American Mathematical Society