Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the Walsh-Fourier series $ \sum {{a_k}{w_k}(x)} $ of a function $ f$ assumed to be of bounded fluctuation on the interval $ [0,1)$. 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 $ f(x)$ at a point $ x \in [0,1)$ 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.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42C10, 41A30

Retrieve articles in all journals with MSC: 42C10, 41A30


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1123663-0
PII: S 0002-9939(1993)1123663-0
Keywords: Rademacher functions, Walsh functions in the Paley enumeration, Walsh-Fourier series, pointwise convergence, rate of convergence, uniform convergence, $ W$-continuity, bounded fluctuation, bounded variation, Walsh-Dirichlet kernel, Dirichlet-Jordan test
Article copyright: © Copyright 1993 American Mathematical Society