K-SPHERICAL FUNCTIONS ON ABELIAN SEMIGROUPS. Issue 3 (13th June 2017) - ŁUKASIK, RADOSŁAW
Abstract : We present the form of the solutions f:S→ C of the functional equation eqnarray_[STIX]x1D706Kf(x+[STIX]x1D706y)=|K|f(x)f(y)for x, yS, eqnarray where f satisfies the condition f(_[STIX]x1D706K[STIX]x1D706x)≠ 0 for all xS, (S, +) is an abelian semigroup and K is a subgroup of the automorphism group of S .