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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.

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The nonlocal nature of the summability of Fourier series by certain absolute Riesz methods
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by David Borwein PDF
Proc. Amer. Math. Soc. 114 (1992), 89-94 Request permission

Abstract:

It is proved that for a large class of sequences $\{ {{\lambda _n}} \}$ the summability at a point of a Fourier series $\Sigma A_n ( t )$ by the absolute Riesz method $| {R,{\lambda _n},1} |$ is not a local property of the generating function. It is also proved, inter alia, that, for every $\varepsilon > 0$, the $| {R,{\lambda _n},1} |$ summability of the factored series $\Sigma A_n ( t )\lambda _n^{ - \varepsilon }$ at any point is always a local property of the generating function.
References
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 114 (1992), 89-94
  • MSC: Primary 42A28
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1062383-7
  • MathSciNet review: 1062383