This article is cited in 2 papers

Generalized Convolution Roots of Positive Definite Kernels on Complex Spheres

Victor S. Barbosa, Valdir A. Menegatto

Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970, São Carlos - SP, Brasil

Abstract: Convolution is an important tool in the construction of positive definite kernels on a manifold. This contribution provides conditions on an $L^2$-positive definite and zonal kernel on the unit sphere of $\mathbb{C}^q$ in order that the kernel can be recovered as a generalized convolution root of an equally positive definite and zonal kernel.

Keywords: positive definiteness; zonal kernels; recovery formula; convolution roots; Zernike or disc polynomials.

MSC: 33C55; 41A35; 41A63; 42A82; 42A85

Received: October 16, 2014; in final form February 10, 2015; Published online February 13, 2015

Language: English

DOI: 10.3842/SIGMA.2015.014

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ArXiv: 1410.4125