The Skitovich-Darmois equation in the classes of continuous and measurable functions

DOI10.1134/S1064562406050218zbMath1140.43004OpenAlexW2004168454MaRDI QIDQ5920475

Margaryta Myronyuk, Gennadiy Feldman

Publication date: 13 March 2008

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562406050218

zbMATH Keywords

Gaussianpositive definite functionslocally compact abelian groupsSkitovich-Darmois equation

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Positive definite functions on groups, semigroups, etc. (43A35) Analysis on specific locally compact and other abelian groups (43A70)

Cites Work

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• Note on the equation \(f(x)g(y)=h(ax+by)k(cx+dy)\) and generalized quadratic polynomials
• On the functional equation f(x)g(y)=h(ax+by)k(cx+dy)
• A characterization of the Gaussian distribution on Abelian groups
• On the Skitovich-Darmois theorem for compact Abelian groups
• On the functional equation \(f(x)g(y) = \prod\limits_{i=1}^n h_i (a_i x + b_i y)\)
• Generalized Gaussian measure and a 'functional equation'. I
• On single-product functions with rotational symmetry

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