Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

 

Fourier series of functions of $\Lambda$-bounded variation
HTML articles powered by AMS MathViewer

by Daniel Waterman PDF
Proc. Amer. Math. Soc. 74 (1979), 119-123 Request permission

Abstract:

It is shown that the Fourier coefficients of functions of $\Lambda$-bounded variation, $\Lambda = \{ {\lambda _n}\}$, are $O({\lambda _n}/n)$. This was known for ${\lambda _n} = {n^{\beta + 1}}, - 1 \leqslant \beta < 0$. The classes L and HBV are shown to be complementary, but L and $\Lambda {\text {BV}}$ are not complementary if $\Lambda {\text {BV}}$ is not contained in HBV. The partial sums of the Fourier series of a function of harmonic bounded variation are shown to be uniformly bounded and a theorem analogous to that of Dirichlet is shown for this class of functions without recourse to the Lebesgue test.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A16, 42A20
  • Retrieve articles in all journals with MSC: 42A16, 42A20
Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 74 (1979), 119-123
  • MSC: Primary 42A16; Secondary 42A20
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0521884-1
  • MathSciNet review: 521884