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GENERALIZED FOURIER EXPANSIONS OF DIFFERENTIABLE FUNCTIONS ON THE SPHERE

Published online by Cambridge University Press:  27 July 2005

FRANCISCO JAVIER GONZÁLEZ VIELI
FRANCISCO JAVIER GONZÁLEZ VIELI
Affiliation:
École Polytechnique Fédérale de Lausanne, SB/IACS/CAHRU, MA B1 513, Station 8, 1015 Lausanne, Switzerland e-mail: [email protected]
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Abstract

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We show that the Fourier expansion in spherical $h$-harmonics (from Dunkl's theory) of a function $f$ on the sphere converges uniformly to $f$ if this function is sufficiently differentiable.

Keywords

Primary 42C10Secondary 33C50
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue 2 , May 2005 , pp. 339 - 345
Copyright
2005 Glasgow Mathematical Journal Trust