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Estimations of the remainder of spherical harmonic series

Published online by Cambridge University Press:  01 July 2008

XIRONG CHANG ,
FENG DAI  and
KUNYANG WANG
XIRONG CHANG
Affiliation:
Department of Mathematics and Physics, North China Electrical Power University, Beijing 102206, China. e-mail: zhxir@ncepubj.edu.cn
FENG DAI
Affiliation:
Department of Mathematical and Statistical Sciences, CAB 632, University of Alberta, Edmonton, Alberta, CanadaT6G 2G1. e-mail: dfeng@math.ualberta.ca
KUNYANG WANG*
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China. e-mail: wangky@bnu.edu.cn
*
‡Corresponding author, partially supported by NNSF of China under the grant # 10471010(2005–2007).
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Abstract

An asymptotic estimate is obtained for the error in approximation of functions by partial sums of spherical harmonic expansions. The precise constant in the main term is found and the order of growth of the remainder term is given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 1 , July 2008 , pp. 243 - 255
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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