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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

What strong monotonicity condition on Fourier coefficients can make the ratio $ \Vert f-S\sb n(f)\Vert /E\sb n(f)$ be bounded?


Author: S. P. Zhou
Journal: Proc. Amer. Math. Soc. 121 (1994), 779-785
MSC: Primary 42A10; Secondary 42A20, 42A32
MathSciNet review: 1198461
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Abstract: Let $ \{ {\phi _n}\} _{n = 1}^\infty $ be a positive increasing sequence and $ {\phi _n}\hat f(n)$ decrease. We ask what exact conditions on $ \{ {\phi _n}\} $ make $ \left\Vert {f - {S_n}(f)} \right\Vert/{E_n}(f)$ bounded? The present paper will give a complete answer to it.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1198461-3
PII: S 0002-9939(1994)1198461-3
Keywords: Approximation, Fourier sums, coefficients, strong monotonicity
Article copyright: © Copyright 1994 American Mathematical Society