Search results for "HAar and Walsh series"

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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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