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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the rate of growth of the Walsh antidifferentiation operator


Author: R. Penney
Journal: Proc. Amer. Math. Soc. 55 (1976), 57-61
DOI: https://doi.org/10.1090/S0002-9939-1976-0397289-0
MathSciNet review: 0397289
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Abstract: In [1] Butzer and Wagner introduced a concept of differentiation and antidifferentiation of Walsh-Fourier series. Antidifferentiation is accomplished by convolving (in the sense of the Walsh group) against a function $ \Omega $. In this paper we study growth and the continuity properties of $ \Omega $ showing that $ \Omega $ is bounded from below by $ - 1$, is continuous in $ (0,1)$ and grows at most like $ \log 1/x$ as $ x \to 0$. We use this information to study continuity properties of differentiable functions.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0397289-0
Keywords: Walsh functions, antidifferentiation
Article copyright: © Copyright 1976 American Mathematical Society

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