Search results for "Walsh serie"

showing 2 items of 2 documents

Multidimensional P-adic Integrals in some Problems of Harmonic Analysis

2017

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.

rectangular convergencequasi-measureHaar seriePerron P-adic integralWalsh serieHenstock-Kurzweil integralSaks continuityVilenkin serie
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Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals in the theory of Haar and Walsh series

2015

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.

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 functionsymbolsUniquenessAnalysisMathematicsJournal of Mathematical Analysis and Applications
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