A quantitative DirichletJordan test for WalshFourier series
Author:
Ferenc Móricz
Journal:
Proc. Amer. Math. Soc. 118 (1993), 143149
MSC:
Primary 42C10; Secondary 41A30
MathSciNet review:
1123663
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Abstract: We consider the WalshFourier 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 WalshFourier 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 DirichletJordan test and a global convergence result due to Onneweer.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199311236630
PII:
S 00029939(1993)11236630
Keywords:
Rademacher functions,
Walsh functions in the Paley enumeration,
WalshFourier series,
pointwise convergence,
rate of convergence,
uniform convergence,
continuity,
bounded fluctuation,
bounded variation,
WalshDirichlet kernel,
DirichletJordan test
Article copyright:
© Copyright 1993
American Mathematical Society
