Convergence rate of spherical harmonic expansions of smooth functions |
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| Authors: | Feng Dai |
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| Affiliation: | a Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
b School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China |
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| Abstract: | We extend a well-known result of Bonami and Clerc on the almost everywhere (a.e.) convergence of Cesàro means of spherical harmonic expansions. For smooth functions measured in terms of φ-derivatives on the unit sphere, we obtained the sharp a.e. convergence rate of Cesàro means of their spherical harmonic expansions. |
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| Keywords: | Almost everywhere convergence Spherical harmonics Cesà ro means φ-Derivatives |
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