Prépublication A.O.C. numéro 01-02 (06.06.2001)

Generalized function algebras as sequence space algebras
Antoine Delcroix - Laboratoire A.O.C., Université des Antilles et de la Guyane, F-97159, Pointe-à-Pitre cedex
Maximilian F. Hasler - Laboratoire A.O.C., Université Antilles-Guyane, B.P. 7209, F-97275 Schoelcher cedex
Stevan Pilipovic - Inst. of Mathematics, University of Novi Sad, 21000 Novi Sad (Yougoslavia).
Vincent Valmorin - Laboratoire A.O.C., Université des Antilles et de la Guyane, F-97159 Pointe-à-Pitre cedex

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 discrete topology on the basic space. This result is in analogy to Schwartz' impossibility result concerning multiplication of distributions.