2001•Mathematical Proceedings of the Cambridge Philosophical SocietyRequires access

Colombeau generalized ultradistributions

Stevan Pilipović, Dimitris Scarpalézos

Abstract

An algebra of Colombeau generalized ultradistributions in which the corresponding space of ultradistributions is embedded via regularizations and in which the multiplication of ultradifferentiable functions of an appropriate class is the ordinary multiplication is constructed. This enables the development of the local and micro-local analysis in the framework of a new scale of Colombeau algebras. Sufficient conditions for a generalized ultradistribution being an ultradifferentiable function are given.

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Key concepts: Multiplication (music), Generalized function, Class (philosophy), Mathematics, Algebra over a field, Pure mathematics, Function (biology), Space (punctuation)