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.References
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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