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

zbMath1272.42004MaRDI QIDQ1928871

Semyon Alesker, Dmitry Faifman, Vitali D. Milman, Shiri Artstein-Avidan

Publication date: 4 January 2013

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ijm/1336049986

zbMATH Keywords

Fourier transformconvolutionproducttempered distributionSchwartz space

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

Related Items (11)

Rigidity of the Chain Rule and Nearly Submultiplicative Functions ⋮ The chain rule as a functional equation ⋮ On the Fourier transform on function algebras on locally compact abelian groups ⋮ Convex geometry and its applications. Abstracts from the workshop held December 12--18, 2021 (hybrid meeting) ⋮ Submultiplicative Operators on Ck-Spaces ⋮ Integral transforms characterized by convolution ⋮ Order preserving and order reversing operators on the class of convex functions in Banach spaces ⋮ The derivation equation for \(C^k\)-functions: stability and localization ⋮ Operator Functional Equations in Analysis ⋮ Characterizing the derivative and the entropy function by the Leibniz rule ⋮ The chain rule functional equation on \(\mathbb R^n\)

Cites Work

• A characterization of the concept of duality
• A characterization of the Fourier transform and related topics
• The concept of duality in convex analysis, and the characterization of the Legendre transform
• A characterization of Fourier transforms
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