6533b820fe1ef96bd127a622

RESEARCH PRODUCT

Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals in the theory of Haar and Walsh series

Francesco TuloneValentin A. Skvortsov

subject

Pure mathematicsBasis (linear algebra)Series (mathematics)Applied MathematicsMathematical analysisMathematics::Classical Analysis and ODEsHaarFunction (mathematics)Type (model theory)HAar and Walsh seriesKurzweil-Henstock integral Perron integralsymbols.namesakeFourier transformSettore MAT/05 - Analisi MatematicaWalsh functionsymbolsUniquenessAnalysisMathematics

description

Abstract The problem of recovering the coefficients of rectangular convergent multiple Haar and Walsh series from their sums, by generalized Fourier formulas, is reduced to the one of recovering a function (the primitive) from its derivative with respect to the appropriate derivation basis. Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals are compared and it is shown that a Perron-type integral, defined by major and minor functions having a special continuity property, solves the coefficients problem for series which are convergent everywhere outside some uniqueness sets.

yearjournalcountryeditionlanguage
2015-01-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2014.08.002