Title: Convergence and Divergence of A Class of Generalized Fourier Series
Abstract: In this paper,the pointwise convergence and divergence of a class of generalized Fourier series generated by piecewise linear spectral sequences are studied.For a class of functions,the rate of decay of generalized Fourier coefficients is estimated.Some criteria for pointwise convergence of generalized Fourier series are given.Two negative results are presented.One is that there exist 1-periodic continuous functions whose generalized Fourier series diverge at some point.The other is that there exist 1-periodic integrable functions whose generalized Fourier series diverge everywhere.
Publication Year: 2007
Publication Date: 2007-01-01
Language: en
Type: article
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