Spectrum of Positive Definite Functions on Product Hypergroups
نویسندگان
چکیده
This paper aims to show that the amenability of K1 ×K2 is equivalent to the following condition: “If φ is a continuous positive definite function defined on K1 ×K2 and φ ≥ 0 then the constant function 1K1×K2 belongs to the spectrum of φ”, which K1 and K2 are locally compact hypergroups as defined by R. Jewett [1], with convolutions ∗1, ∗2 respectively.Our study deals with the cases of exponentially bounded product hypergroups and discrete solvable product hypergroups. And study of conditionally exponential convex functions.
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