A quantitative Dirichlet-Jordan test for Walsh-Fourier series

Author:
Ferenc Móricz

Journal:
Proc. Amer. Math. Soc. **118** (1993), 143-149

MSC:
Primary 42C10; Secondary 41A30

MathSciNet review:
1123663

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Abstract: We consider the Walsh-Fourier series of a function assumed to be of bounded fluctuation on the interval . Every function of bounded variation is also of bounded fluctuation on the same interval, but not conversely. We present an estimate for the difference of at a point and the partial sum of its Walsh-Fourier series in terms of the bounded fluctuation operator. This gives rise to a local convergence result. As special cases, we obtain a Walsh analogue of the Dirichlet-Jordan test and a global convergence result due to Onneweer.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1123663-0

Keywords:
Rademacher functions,
Walsh functions in the Paley enumeration,
Walsh-Fourier series,
pointwise convergence,
rate of convergence,
uniform convergence,
-continuity,
bounded fluctuation,
bounded variation,
Walsh-Dirichlet kernel,
Dirichlet-Jordan test

Article copyright:
© Copyright 1993
American Mathematical Society