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Hyers-Ulam stability of spherical functions. (English) Zbl 1338.39035

Summary: In [Publ. Math. 69, No. 1–2, 95–120 (2006; Zbl 1111.39021)] we obtained the Hyers-Ulam stability of the functional equation \[ \int_{K}\int_{G} f(xtk\cdot y)d\mu (t)dk=f(x)g(y),\quad x, y\in G, \] where \(G\) is a Hausdorff locally compact topological group, \(K\) is a compact subgroup of morphisms of \(G\), \(\mu\) is a \(K\)-invariant complex measure with compact support, provided that the continuous function \(f\) satisfies some Kannappan type condition. The purpose of this paper is to remove this restriction.

MSC:

39B52 Functional equations for functions with more general domains and/or ranges
39B82 Stability, separation, extension, and related topics for functional equations

Citations:

Zbl 1111.39021
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Full Text: DOI

References:

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