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Orthogonal polynomials and summability in Fourier orthogonal series on spheres and on balls

Published online by Cambridge University Press:  26 October 2001

YUAN XU
YUAN XU
Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222, U.S.A. e-mail: yuan@math.uoregon.edu
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Abstract

For a general family of weight functions, a relation between orthogonal polynomials on the unit sphere in ℝd+m and orthogonal polynomials on the unit ball in ℝd is discussed and used to show that the summability of the Fourier orthogonal series on the unit ball follows from the summability on the unit sphere. Convergence of the Cesàro summability is established for a number of weight functions on the sphere and on the ball.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 131 , Issue 1 , July 2001 , pp. 139 - 155
Copyright
2001 Cambridge Philosophical Society

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