Geodesic
Multidimensional P-adic Integrals in some Problems of Harmonic Analysis
Minimax theory and its applications, Tome 2 (2017) no. 1
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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.
Mots-clés : Henstock-Kurzweil integral, Perron P-adic integral, Vilenkin series, Walsh series, Haar series, rectangular convergence, Saks continuity, quasi-measure 
@article{MTA_2017_2_1_a8,
     author = {Francesco Tulone,Valentin Skvortsov},
     title = {Multidimensional {P-adic} {Integrals} in some {Problems} of {Harmonic} {Analysis}},
     journal = {Minimax theory and its applications},
     year = {2017},
     volume = {2},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/MTA_2017_2_1_a8/}
}
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Francesco Tulone,Valentin Skvortsov. Multidimensional P-adic Integrals in some Problems of Harmonic Analysis. Minimax theory and its applications, Tome 2 (2017) no. 1. http://geodesic.mathdoc.fr/item/MTA_2017_2_1_a8/