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Generalized function algebras as sequence space algebras

Authors: Antoine Delcroix, Maximilian F. Hasler, Stevan Pilipovic and Vincent Valmorin
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 2031-2038
MSC (2000): Primary 46A45, 46F30; Secondary 46E10, 46A13, 46A50, 46E35, 46F05
Published electronically: February 12, 2004
MathSciNet review: 2053975
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Abstract | References | Similar Articles | Additional Information

Abstract: A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of exponential weights. Such an algebra with embedded Dirac's delta distribution induces the discrete topology on the basic space.

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Additional Information

Antoine Delcroix
Affiliation: IUFM des Antilles et de la Guyane, Morne Ferret, BP 399, 97159 Pointe à Pitre cedex, Guadeloupe, F.W.I.

Maximilian F. Hasler
Affiliation: Dépt. Scientifique Interfacultaire, Université des Antilles et de la Guyane, BP 7209, 97275 Schoelcher cedex, Martinique, F.W.I.

Stevan Pilipovic
Affiliation: Faculty of Sciences and Mathematics, University of Novi Sad, Trg D. Obradovića 4, 21000 Novi Sad, Yugoslavia

Vincent Valmorin
Affiliation: Faculté des Sciences Exactes et Naturelles, Université des Antilles et de la Guyane, Campus de Fouillole, 97159 Pointe à Pitre cedex, Guadeloupe, F.W.I.

Received by editor(s): May 8, 2002
Received by editor(s) in revised form: March 19, 2003
Published electronically: February 12, 2004
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society

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