\alpha-Amenable Hypergroups
Let $K$ denote a locally compact commutative hypergroup, $L^1(K)$ the hypergroup algebra, and $\alpha$ a real-valued hermitian character of $K$. We show that $K$ is $\alpha$-amenable if and only if $L^1(K)$ is $\alpha$-left amenable. We also consider the $\alpha$-amenability of hypergroup joins and polynomial hypergroups in several variables as well as a single variable.
disc polynomials, Mathematics - Functional Analysis, 43A62, 43A07, 46H20, \(\alpha \)-amenable hypergroups, Mathematics - Classical Analysis and ODEs, Means on groups, semigroups, etc.; amenable groups, Koornwinder, associated Legendre, Pollaczek, Structure, classification of topological algebras, Harmonic analysis on hypergroups
disc polynomials, Mathematics - Functional Analysis, 43A62, 43A07, 46H20, \(\alpha \)-amenable hypergroups, Mathematics - Classical Analysis and ODEs, Means on groups, semigroups, etc.; amenable groups, Koornwinder, associated Legendre, Pollaczek, Structure, classification of topological algebras, Harmonic analysis on hypergroups
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