Regularity properties of polynomials on groups

DOI10.1007/BF01955017zbMath0578.39004OpenAlexW2057976098MaRDI QIDQ1066366

László Székelyhidi

Publication date: 1985

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01955017

zbMATH Keywords

polynomialslinear functional equationsregularity propertiescontinuousCauchylocally convexFréchetlocally boundedcommutative topological groupsmeasurable set of positive measurePexider

Mathematics Subject Classification ID

Functional equations for functions with more general domains and/or ranges (39B52) Analysis on specific locally compact and other abelian groups (43A70)

Related Items (9)

Regularization and general methods in the theory of functional equations ⋮ A functional definition of polynomial for connected Lie groups ⋮ Derivations and linear functions along rational functions ⋮ Mean-value type functional equations ⋮ Characterizations of derivations ⋮ Polynomial and horizontally polynomial functions on Lie groups ⋮ An alternative equation for polynomial functions ⋮ A result concerning the stability of some difference equations and its applications ⋮ Regularity properties of exponential polynomials on groups

Cites Work

• Unnamed Item
• A property of a set of positive measure and its application
• General and regular solutions of functional equations characterizing harmonic polynomials
• Boundedness on a set of positive measure and the mean value property characterizes polynomials on a space \(V^ n\)
• On vanishing n-th ordered differences and Hamel bases
• A representation theorem for $(X_1-1)(X_2-1)...(X_n-1)$ and its applications
• On the functional equation f(x+y) =f(x) +f(y)

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