Minimax Theory and its Applications 02 (2017), No. 1, 153--174
Copyright Heldermann Verlag 2017
Multidimensional P-adic Integrals in some Problems of Harmonic Analysis
Francesco Tulone
Dept. of Mathematics, University of Palermo, Palermo, Italy
francesco.tulone@unipa.it
Valentin Skvortsov
Dept. of Mathematics, Moscow State University, Moscow 119991, Russia
vaskvor2000@yahoo.com
The paper is a survey of results related to the problem of recovering the coefficients of some classical orthogonal series from their sums by generalized Fourier formulas. The method is based on reducing the coefficient problem to the one of recovering a function from its derivative with respect to an appropriate derivation basis. In the case of the multiple Vilenkin system the problem is solved by using a multidimensional P-adic integral.
Keywords: Henstock-Kurzweil integral, Perron P-adic integral, Vilenkin series, Walsh series, Haar series, rectangular convergence, Saks continuity, quasi-measure.
MSC: 26A39; 42C10
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