The Gibbs phenomenon for general Franklin systems |
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Authors: | V G Mikayelyan |
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Institution: | 1.Yerevan State University,Yerevan,Armenia |
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Abstract: | The paper is devoted to the Gibbs phenomenon for series by general Franklin systems. The general Franklin system corresponding to a given dense sequence of points T = (t n , n ≥ 0) in 0, 1] is a sequence of orthonormal piecewise linear functions with knots from T, that is, the nth function from the system has knots t 0,..., t n . The main result of this paper is that the Gibbs phenomenon for Fourier series by general Franklin systems occurs for almost all points of 0, 1]. |
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