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THE DECAY OF THE WALSH COEFFICIENTS OF SMOOTH FUNCTIONS

Part of: Nontrigonometric harmonic analysis

Published online by Cambridge University Press:  02 July 2009

JOSEF DICK
JOSEF DICK*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia (email: josef.dick@unsw.edu.au)
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Abstract

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We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and nonperiodic reproducing kernel Hilbert spaces. A lower bound which shows that our results are best possible is also shown.

Keywords

waveletWalsh seriesWalsh coefficientsobolev spacesmooth function

MSC classification

Secondary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 3 , December 2009 , pp. 430 - 453
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

References

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