D'Alembert's equation and spherical functions

DOI10.1007/BF01832986zbMath0810.39008MaRDI QIDQ1339672

Henrik Stetkaer

Publication date: 7 December 1994

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/137608

zbMATH Keywords

groupsspherical functionseigenfunctionsbounded solutionsd'Alembert's functional equationWilson's functional equations

Mathematics Subject Classification ID

Functional equations for functions with more general domains and/or ranges (39B52) Harmonic analysis and spherical functions (43A90)

Related Items (15)

Hyers-Ulam stability of spherical functions ⋮ Wilson's functional equations on groups ⋮ Functional equations on abelian groups with involution ⋮ On a signed cosine equation of \(N\) summands ⋮ Hyers–Ulam–Rassias Stability of the Generalized Wilson’s Functional Equation ⋮ Superstability problem for a large class of functional equations ⋮ On solutions of the d'Alembert equation on a restricted domain ⋮ On uniformly bounded spherical functions in Hilbert space ⋮ D'Alembert's and Wilson's equations on semigroups ⋮ Operatorial approach to the non-Archimedean stability of a Pexider K-quadratic functional equation ⋮ Wilson's functional equation on \(\mathbb{C}\) ⋮ Superstability of functional equations related to spherical functions ⋮ A note on d'Alembert's functional equation ⋮ Solutions and stability of generalized Kannappan's and Van Vleck's functional equations ⋮ The superstability of d'Alembert's functional equation on the Heisenberg group

Cites Work

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• Almost periodicity and functional equations
• On D'Alembert's functional equation on an Abelian group
• Bounded \(K\)-spherical functions on Heisenberg groups
• On functional equations associated with characters of unitary representations of groups
• The cosine functional equation for nilpotent groups
• A solution of D'Alembert's functional equation on a locally compact Abelian group
• A class of symmetric and a class of Wiener group algebras
• On Gelfand Pairs Associated with Solvable Lie Groups
• The D'Alembert Functional Equation
• Harmonic Analysis in Phase Space. (AM-122)
• On the Functional Equation f(x + y) + f(x - y) = 2f(x)f(y)
• The Functional Equation f(xy) + f(xy -1 ) = 2f(x)f(y) for Groups

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