Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 15 (2019), 004, 12 pages      arXiv:1807.08184      https://doi.org/10.3842/SIGMA.2019.004

Relations between Schoenberg Coefficients on Real and Complex Spheres of Different Dimensions

Pier Giovanni Bissiri a, Valdir A. Menegatto b and Emilio Porcu ac
a) School of Mathematics & Statistics, Newcastle University, Newcastle Upon Tyne, NE1 7RU, UK
b) Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970, São Carlos - SP, Brazil
c) Department of Mathematics, University of Atacama, Copiapó, Chile

Received July 25, 2018, in final form January 18, 2019; Published online January 23, 2019

Abstract
Positive definite functions on spheres have received an increasing interest in many branches of mathematics and statistics. In particular, the Schoenberg sequences in the spectral representation of positive definite functions have been studied by several mathematicians in the last years. This paper provides a set of relations between Schoenberg sequences defined over real as well as complex spheres of different dimensions. We illustrate our findings describing an application to strict positive definiteness.

Key words: positive definite; Schoenberg pair; spheres; strictly positive definite.

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