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

DOI10.1016/J.JMAA.2014.08.002zbMath1301.26011OpenAlexW1995216003MaRDI QIDQ743216

Francesco Tulone, Valentin A. Skvortsov

Publication date: 23 September 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.08.002

zbMATH Keywords

Haar seriesWalsh seriesderivation basescoefficients problemKurzweil-Henstock dyadic integralPerron dyadic integralSaks continuity of interval functions

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Denjoy and Perron integrals, other special integrals (26A39)

Related Items (9)

The \(L^r\)-variational integral ⋮ On descriptive characterizations of an integral recovering a function from its \(L^r\)-derivative ⋮ On \(U\)- and \(M\)-sets for series with respect to characters of compact zero-dimensional groups ⋮ Integration of Banach-valued functions and Haar series with Banach-valued coefficients ⋮ \(\mathcal V\)-sets in the products of zero-dimensional compact abelian groups ⋮ Non-uniqueness for rearranged double Haar series ⋮ A version of Hake's theorem for Kurzweil-Henstock integral in terms of variational measure ⋮ Unnamed Item ⋮ The 𝐻𝐾ᵣ-integral is not contained in the 𝑃ᵣ-integral

Cites Work

• Derivation bases on the real line. I
• A constructive variant of the definition of an HD-integral
• Une théorie de Denjoy des martingales dyadiques. (A Denjoy theory of dyadic martingales)
• Uniqueness sets for multiple Haar series
• On continuous major and minor functions for the \(n\)-dimensional Perron integral
• Generalized Hake property for integrals of Henstock type
• Henstock type integral in harmonic analysis on zero-dimensional groups
• Recovery of the coefficients of multiple Haar and Walsh series
• Henstock integration in the plane
• Recent developments in the theory of Haar series
• Uniqueness and Quasi-Measures on the Group of Integers of A p-Series Field
• Several properties of generalized multivariate integrals and theorems of the du Bois-Reymond type for Haar series
• ON CERTAIN CLASSES OF SETS OF UNIQUENESS OF MULTIPLE WALSH SERIES
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