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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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Wild behaviour via plane sets: dense-image operators
by
María-del-Carmen Calderón-Moreno
Universidad de Sevilla (Spain)
Coauthors: Luis Bernal-González (Universidad de Sevilla)

Given an open subset G of the complex plane, we give suitable conditions that differential-antidifferential operators have a wild behaviour near the boundary of G via certain subsets A subset G. From those, we introduce the dense-image operators T on the space H(G) of holomorphic functions on G. The relationship with other kinds of operators with wild behaviour is studied, proving that the new concept generalizes the earlier one of omnipresent but there is no good relationship with the strongly omnipresent operators. We obtain sufficient conditions under which an operator is dense-image and, with those, we completely characterize holomorphic mappings generating dense-image composition and multiplication operators. In addition, we show that the onto linear operators and the Volterra complex integral operators plus infinite order differential operators are dense-image.

(T)

Date received: November 29, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cado-39.