On multiplicative maps of continuous and smooth functions

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

In this note, we study the general form of a multiplicative bijection on several families of functions defined on manifolds, both real or complex valued. In the real case, we prove that it is essentially defined by a composition with a diffeomorphism of the underlying manifold (with a bit more freedom in families of continuous functions). Our results in the real case are mostly simple extensions of known theorems. We then show that in the complex case, the only additional freedom allowed is complex conjugation. Finally, we apply those results to characterize the Fourier transform between certain function spaces.

Original languageEnglish
Title of host publicationGeometric Aspects of Functional Analysis
Subtitle of host publicationIsrael Seminar 2006-2010
PublisherSpringer Verlag
Pages35-59
Number of pages25
ISBN (Print)9783642298486
DOIs
StatePublished - 2012

Publication series

NameLecture Notes in Mathematics
Volume2050
ISSN (Print)0075-8434

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