Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

On the magnitude of Fourier coefficients


Authors: Michael Schramm and Daniel Waterman
Journal: Proc. Amer. Math. Soc. 85 (1982), 407-410
MSC: Primary 42A16; Secondary 26A45
DOI: https://doi.org/10.1090/S0002-9939-1982-0656113-1
MathSciNet review: 656113
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $f$ is a function on ${R^1}$ of $\Lambda$-bounded variation and period $2\pi$, then its $n$th Fourier coefficient $\hat f(n) = O(1/\Sigma _1^n1/{\lambda _j})$ and its integral modulus of continuity ${\omega _1}(f;\delta ) = O(1/\Sigma _1^{[1/\delta ]}1/{\lambda _j})$. The result on $\hat f(n)$ is best possible in a sense. These results can be extended to certain other classes of functions of generalized variation.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A16, 26A45

Retrieve articles in all journals with MSC: 42A16, 26A45


Additional Information

Article copyright: © Copyright 1982 American Mathematical Society