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
*Butzer, P.L., Wagner, H.J., “Walsh-Fourier series and the concept of a derivative”, Applicable Analysis, Vol. 3, 1973, 29-46.
Edwards, R.E., Gaudry, G.I., Littlewood-Paley and Multiplier Theory, Springer Verlag, Berlin, 1977.
Kitada, T., “Potential operators and multipliers on locally compact Vilenkin groups”, Bull. Austral. Math. Soc., Vol. 54, 1996, 459-471.
Kitada, T., Onneweer, C.W., “Hormander-type multiplier theorems on locally compact Vilenkin groups”, Theory and Applications of Gibbs Derivatives, 1990, 115-125.
Onneweer, C.W., “Differentiation on a p-adic or p-series field”, Linear Spaces and Approximation, ISNM 40, 1978, 197-198.
*Onneweer, C.W., “On the definition of dyadic differentiation”, Applic. Analysis, Vol. 9, 1979, 267-278.
Vilenkin, N. Ya., “On a class of complete orthonormal systems”, Amer. Math. Soc. Transl., Vol. 28, 1963, 1-35.
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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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DOI: https://doi.org/10.2991/978-94-6239-160-4_7
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