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Wilson's functional equations on groups

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Summary

We study properties of solutionsf, g, h ∈ C(G) of the functional equation

$$\int_K {f(xk \cdot y)\overline {x(k)} } dk = g(x)h(y),x,y \in G$$
((1))

and of the special case

$$\int_K {f(xk \cdot y)\overline {x(k)} } dk = g(x)f(y),x,y \in G$$
((2))

whereG is a locally compact group,K a compact subgroup of Aut(G) andχ a character onK. We show thatg andh are associated to certainK-spherical functions and use that to compute the complete set of solutions in special examples; in particular in the case ofG =R n.

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Authors and Affiliations

  1. Department of Mathematics, Aarhus University, Ny Munkegade, DK-8000, Aarhus C, Denmark

    Henrik Stetkaer

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  1. Henrik Stetkaer
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Stetkaer, H. Wilson's functional equations on groups. Aeq. Math. 49, 252–275 (1995). https://doi.org/10.1007/BF01827944

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