Article contents
$K$-SPHERICAL FUNCTIONS ON ABELIAN SEMIGROUPS
Published online by Cambridge University Press: 13 June 2017
Abstract
We present the form of the solutions $f:S\rightarrow \mathbb{C}$ of the functional equation
$$\begin{eqnarray}\mathop{\sum }_{\unicode[STIX]{x1D706}\in K}f(x+\unicode[STIX]{x1D706}y)=|K|f(x)f(y)\quad \text{for }x,y\in S,\end{eqnarray}$$
$f$ satisfies the condition
$f(\sum _{\unicode[STIX]{x1D706}\in K}\unicode[STIX]{x1D706}x)\neq 0$ for all
$x\in S$,
$(S,+)$ is an abelian semigroup and
$K$ is a subgroup of the automorphism group of
$S$.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 96 , Issue 3 , December 2017 , pp. 479 - 486
- Copyright
- © 2017 Australian Mathematical Publishing Association Inc.
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