Positive Definiteness on Products of Compact Two-point Homogeneous Spaces and Locally Compact Abelian Groups

Author(s)

Menegatto, V. A. ^[1] ; Oliveira, C. P. ^[2]

Affiliation

^[1] ICMC USP Sao Carlos, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Fed Itajuba, Inst Matemat & Comp, BR-37500903 Itajuba, MG - Brazil

• Document type: Journal article
• Source: CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES; v. 63, n. 4, p. 705-715, DEC 2020.
• Web of Science Citations: 0

Abstract

In this paper, we consider the problem of characterizing positive deunite functions on compact two-point homogeneous spaces cross locally compact abelian groups. For a locally compact abelian group G with dual group (G) over cap, a compact two-point homogeneous space H with normalized geodesic distance delta and a proule function phi: {[}-1, 1] x G -> C satisfying certain continuity and integrability assumptions, we show that the positive deuniteness of the kernel ((x, u), (y, v)) > is an element of (H x G)(2) bar right arrow phi (cos delta(x, y), uv(-1)) is equivalent to the positive deuniteness of the Fourier transformed kernels (x, y) is an element of H-2 bar right arrow (phi) over cap (cos delta) ((x, y)) (gamma), gamma is an element of (G) over cap, where t(u) = phi(t)(t, u), u is an element of G. We also provide some results on the strict positive deuniteness of the kernel. (AU)

• FAPESP's process: 16/09906-0 - Harmonic analysis, approximation theory and applications
• Grantee: Dimitar Kolev Dimitrov
• Support Opportunities: Research Projects - Thematic Grants