Illinois Journal of Mathematics

A characterization of product preserving maps with applications to a characterization of the Fourier transform

S. Alesker, S. Artstein-Avidan, D. Faifman, and V. Milman

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Abstract

It is shown that a product preserving bijective (not necessarily real linear or continuous) operator on an appropriate class of complex valued functions must have either the form $[\phi\mapsto \phi\circ u]$ or $[\phi\mapsto\overline{\phi\circ u}]$ where $u$ is a fixed diffeomorphism of the base.

Article information

Source
Illinois J. Math., Volume 54, Number 3 (2010), 1115-1132.

Dates
First available in Project Euclid: 3 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1336049986

Digital Object Identifier
doi:10.1215/ijm/1336049986

Mathematical Reviews number (MathSciNet)
MR2928347

Zentralblatt MATH identifier
1272.42004

Subjects
Primary: 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Citation

Alesker, S.; Artstein-Avidan, S.; Faifman, D.; Milman, V. A characterization of product preserving maps with applications to a characterization of the Fourier transform. Illinois J. Math. 54 (2010), no. 3, 1115--1132. doi:10.1215/ijm/1336049986. https://projecteuclid.org/euclid.ijm/1336049986


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References

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