Skip to Main Content

Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Summability methods fail for the $2^{n}th$ partial sums of Fourier series
HTML articles powered by AMS MathViewer

by D. J. Newman PDF
Proc. Amer. Math. Soc. 45 (1974), 300-302 Request permission

Abstract:

Although the Fourier series of a continuous function need not converge everywhere, it was an important discovery of Fejér that this series must be Cesàro summable. Indeed, it is a frequent occurrence that convergence may be restored to an expansion by use of an appropriate summability method. What we show in this note is that the very opposite phenomenon can occur. Namely, that if one considers only the ${2^n}$th partial sums of the Fourier series, there is no summability method whatever which produces convergence for all continuous functions.
References
  • R. E. Edwards, Fourier series: a modern introduction. Vol. II, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1967. MR 0222538
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A24
  • Retrieve articles in all journals with MSC: 42A24
Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 45 (1974), 300-302
  • MSC: Primary 42A24
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0358200-X
  • MathSciNet review: 0358200