Summability of Fourier-Laplace Series with the Method of Lacunary Arithmetical Means at Lebesgue Points |
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Authors: | Feng Dai Kun Yang Wang |
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Affiliation: | (1) Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China, E-mail: wangky@bnu.edu.cn, CN |
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Abstract: | Let ∑ n −1 be the unit sphere in the n-dimensional Euclidean space ℝ n . For a funcion ƒ∈L(∑ n −1) denote by σδ N (ƒ) the Cesàro means of order δ of the Fourier-Laplace series of ƒ. The special value of δ is known as the critical index. In the case when n is even, this paper proves the existence of the ‘rare’ sequence {n k } such that the summability takes place at each Lebesgue point satisfying some antipole conditions. Received June 28, 1999, Revised August 11, 1999, Accepted February 16, 2000 |
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Keywords: | Convergence Fourier-Laplace series Spherical harmonics Lebesgue point |
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