Atlas: Regularity of solutions of convolution equations by Carmen Fernandez-Rosell

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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

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Regularity of solutions of convolution equations
by
Carmen Fernández-Rosell
Departamento de Análisis Mateático. Universidad de Valencia.
Coauthors: J. Bonet (Universidad Politécnica de Valencia), A. Galbis (Universidad de Valencia), C. Gómez-Collado (Universidad Politécnica de Valencia), R. Meise (Heinrich-Heine-Universität. Düsseldorf)

Let \omega be a weight function. An ultradistribution \mu in E^'_*(R^N), where * can be either (\omega) or {\omega}, is said to be *-hypoelliptic (resp. *-elliptic) if every solution \nu in D^'_*(R^N) of the convolution equation \nu*\mu = f is an element of E_*(R^N) (resp. is a real analytic function) whenever f is in E_*(R^N) (resp. is a real analytic function). We characterize the *-hypoelliptic ultradistributions and we give necessary conditions for *-ellipticity. If \omega is a strong weight, these conditions are also sufficient. Our results extend previous work of Ehrenpreis and Hörmander.

(T)

Date received: April 7, 2000