Integral operators on the sphere generated by positive definite smooth kernels

Ferreira, J. C.; Menegatto, V. A.; Peron, A. P.

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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Integral operators on the sphere generated by positive definite smooth kernels

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Author(s):	Ferreira, J. C. ^[1] ; Menegatto, V. A. ^[1] ; Peron, A. P. ^[1] Total Authors: 3
Affiliation:	^[1] USP, ICMC, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil Total Affiliations: 1
Document type:	Journal article
Source:	JOURNAL OF COMPLEXITY; v. 24, n. 5-6, p. 632-647, OCT-DEC 2008.
Web of Science Citations:	14
Abstract
We consider integral operators on the unit sphere generated by positive definite kernels. Under smoothness conditions of Lipschitz-type on the kernel, we obtain a decay rate for the eigenvalues of the integral operator. The approach we have chosen is a multi-dimensional version, adapted to the spherical setting, of a known procedure used in the analysis of a similar problem for integral operators on the interval {[}0, 1]. In addition to spectral theory, the critical arguments in the paper involve the use of special covers of the sphere generated by quadrature formulas. The estimates themselves are comparable to others in the literature. (C) 2008 Elsevier Inc. All rights reserved. (AU)

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