
Minimax Theory and its Applications 02 (2017), No. 1, 153174 Copyright Heldermann Verlag 2017 Multidimensional Padic 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 Padic integral. Keywords: HenstockKurzweil integral, Perron Padic integral, Vilenkin series, Walsh series, Haar series, rectangular convergence, Saks continuity, quasimeasure. MSC: 26A39; 42C10 [ Fulltextpdf (215 KB)] for subscribers only. 