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- W2982302287 abstract "Abstract In this paper, we consider the problem of characterizing positive definite functions on compact two-point homogeneous spaces cross locally compact abelian groups. For a locally compact abelian group $G$ with dual group $widehat{G}$ , a compact two-point homogeneous space $mathbb{H}$ with normalized geodesic distance $unicode[STIX]{x1D6FF}$ and a profile function $unicode[STIX]{x1D719}:[-1,1]times Grightarrow mathbb{C}$ satisfying certain continuity and integrability assumptions, we show that the positive definiteness of the kernel $((x,u),(y,v))in (mathbb{H}times G)^{2}mapsto unicode[STIX]{x1D719}(cos unicode[STIX]{x1D6FF}(x,y),uv^{-1})$ is equivalent to the positive definiteness of the Fourier transformed kernels $(x,y)in mathbb{H}^{2}mapsto widehat{unicode[STIX]{x1D719}}_{cos unicode[STIX]{x1D6FF}(x,y)}(unicode[STIX]{x1D6FE})$ , $unicode[STIX]{x1D6FE}in widehat{G}$ , where $unicode[STIX]{x1D719}_{t}(u)=unicode[STIX]{x1D719}(t,u)$ , $uin G$ . We also provide some results on the strict positive definiteness of the kernel." @default.
- W2982302287 created "2019-11-08" @default.
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- W2982302287 date "2019-10-29" @default.
- W2982302287 modified "2023-10-18" @default.
- W2982302287 title "Positive Definiteness on Products of Compact Two-point Homogeneous Spaces and Locally Compact Abelian Groups" @default.
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- W2982302287 doi "https://doi.org/10.4153/s0008439519000663" @default.
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