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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A differentiation theorem for functions defined on the dyadic rationals


Author: R. J. Lindahl
Journal: Proc. Amer. Math. Soc. 30 (1971), 349-352
MSC: Primary 26.40; Secondary 42.00
MathSciNet review: 0284549
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Abstract: In this paper we show that under certain conditions a real-valued function defined on an interval of dyadic rational numbers is a monotone function. One of these conditions involves a generalized differentiability property. From this result we offer a new proof of a conjecture of N. Fine concerning the uniqueness of solution of Walsh series.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0284549-2
PII: S 0002-9939(1971)0284549-2
Keywords: Monotone functions on dyadic rationals, Walsh series, Walsh-Fourier series
Article copyright: © Copyright 1971 American Mathematical Society