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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the degree of approximation of a function by the partial sums of its Fourier series
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by Elaine Cohen PDF
Trans. Amer. Math. Soc. 235 (1978), 35-74 Request permission

Abstract:

When f is a $2\pi$ periodic function with rth order fractional derivative, $r \geqslant 0$, of p-bounded variation, Golubov has obtained estimates of the degree of approximation of f, in the ${L^q}$ norm, $q > p$, by the partial sums of its Fourier series. Here we consider the analogous problem for functions whose fractional derivatives are of $\Phi$-bounded variation and obtain estimates of the degree of approximation in an Orlicz space norm. In a similar manner we shall extend various results that he obtained on degree of approximation in the sup norm.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 235 (1978), 35-74
  • MSC: Primary 42A08
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0461004-9
  • MathSciNet review: 0461004