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Walsh-Fourier coefficients and locally constant functions

Author: William R. Wade
Journal: Proc. Amer. Math. Soc. 87 (1983), 434-438
MSC: Primary 42C10
MathSciNet review: 684633
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Abstract: A condition on the Walsh-Fourier coefficients of a continuous function $ f$ sufficient to conclude that $ f$ is locally constant is obtained. The condition contains certain conditions identified earlier by Bočkarev, Coury, Skvorcov and Wade, and Powell and Wade.

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

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  • [2] J. E. Coury, Walsh series with coefficients tending monotonically to zero, Pacific J. Math. 54 (1974), 1-16. MR 0372520 (51:8727)
  • [3] N. J. Fine, On the Walsh functions, Trans. Amer. Math. Soc. 65 (1949), 372-414. MR 0032833 (11:352b)
  • [4] C. H. Powell and W. R. Wade, Term by term dyadic differentiation, Canad. J. Math.33 (1981), 247-256. MR 608868 (82d:42025)
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  • [6] V. A. Skvorcov and W. R. Wade, Generalizations of some results concerning Walsh series and the dyadic derivative, Anal. Math. 5 (1979), 249-255. MR 549241 (80i:42017)
  • [7] J. L. Walsh, A closed set of normal orthogonal functions, Amer. J. Math. 55 (1923), 5-24. MR 1506485

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Keywords: Walsh functions, Walsh-Dirichlet kernel, dyadic addition, Dini derivates
Article copyright: © Copyright 1983 American Mathematical Society

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