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My Involvement with the Dyadic Derivative

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Part of the book series: Atlantis Studies in Mathematics for Engineering and Science ((ASMES,volume 12))

Abstract

My first encounter with the theory of compact Vilenkin groups occurred in 1968 when my Ph.D. advisor, Professor Daniel Waterman, asked me to read and study the paper [7] in which N. Ya. Vilenkin introduced these groups. This resulted in a series of papers, some of them with D. Waterman as co-author, in which various types of convergence of Vilenkin-Fourier series were discussed.

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References

  1. *Butzer, P.L., Wagner, H.J., “Walsh-Fourier series and the concept of a derivative”, Applicable Analysis, Vol. 3, 1973, 29-46.

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  2. Edwards, R.E., Gaudry, G.I., Littlewood-Paley and Multiplier Theory, Springer Verlag, Berlin, 1977.

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  3. Kitada, T., “Potential operators and multipliers on locally compact Vilenkin groups”, Bull. Austral. Math. Soc., Vol. 54, 1996, 459-471.

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  4. Kitada, T., Onneweer, C.W., “Hormander-type multiplier theorems on locally compact Vilenkin groups”, Theory and Applications of Gibbs Derivatives, 1990, 115-125.

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  5. Onneweer, C.W., “Differentiation on a p-adic or p-series field”, Linear Spaces and Approximation, ISNM 40, 1978, 197-198.

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  6. *Onneweer, C.W., “On the definition of dyadic differentiation”, Applic. Analysis, Vol. 9, 1979, 267-278.

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  7. Vilenkin, N. Ya., “On a class of complete orthonormal systems”, Amer. Math. Soc. Transl., Vol. 28, 1963, 1-35.

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Correspondence to Kees (C.W.) Onneweer .

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(C.W.) Onneweer, K. (2015). My Involvement with the Dyadic Derivative. In: Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 1 Foundations. Atlantis Studies in Mathematics for Engineering and Science, vol 12. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-160-4_7

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