"Tauberian L<sup>1</sup> -convergence classes of fourier series. I" by William O. Bray and Ĉaslav V. Stanojevlc
 

Tauberian L1 -convergence classes of fourier series. I

Abstract

It is shown that the Stanojević [2] necessary and sufficient conditions for L1-convergence of Fourier series of(FORMULA PRESENTED) can be reduced to the classical form. A number of corollaries of a recent Tauberian theorem are obtained for the subclasses of the class of Fourier coefficients satisfying (FORMULA PRESENTED). For Fourier series with coefficients asymptotically even with respect to a sequence (FORMULA PRESENTED), and satisfying (FORMULA PRESENTED) necessary and sufficient conditions for L1-convergence are obtained. In particular for (FORMULA PRESENTED), an important corollary is obtained which connects smoothness of ⨍ with smoothness of (FORMULA PRESENTED). © 1983 American Mathematical Society.

Document Type

Article

DOI

https://doi.org/10.1090/S0002-9947-1983-0678336-3

Keywords

L-convergence of fourier series

Publication Date

1-1-1983

Journal Title

Transactions of the American Mathematical Society

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