Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

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

Valentin Skvortsov
Dept. of Mathematics, Moscow State University, Moscow 119991, Russia

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

[ Fulltext-pdf  (215  KB)] for subscribers only.