Search results for "Haar serie"

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On the Almost Everywhere Convergence of Multiple Fourier-Haar Series

2019

The paper deals with the question of convergence of multiple Fourier-Haar series with partial sums taken over homothetic copies of a given convex bounded set $$W\subset\mathbb{R}_+^n$$ containing the intersection of some neighborhood of the origin with $$\mathbb{R}_+^n$$ . It is proved that for this type sets W with symmetric structure it is guaranteed almost everywhere convergence of Fourier-Haar series of any function from the class L(ln+L)n−1.

40A05Control and OptimizationBounded set (topological vector space)Type (model theory)01 natural sciencesmultiple Fourier-Haar seriesHomothetic transformationCombinatoricssymbols.namesakeSettore MAT/05 - Analisi Matematica0103 physical sciences42C10Almost everywhere0101 mathematicsMathematicsSeries (mathematics)Applied Mathematics010102 general mathematicsRegular polygonAlmost everywhere convergenceFunction (mathematics)Fourier transformsymbols010307 mathematical physicslacunar serieAnalysisJournal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)
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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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