Integration of functions ranging in complex Riesz space and some applications in harmonic analysis

DOI10.1134/S0001434615070032zbMath1329.28025OpenAlexW1759245593MaRDI QIDQ887471

Antonio Boccuto, Valentin A. Skvortsov, Francesco Tulone

Publication date: 26 October 2015

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434615070032

zbMATH Keywords

Henstock-Kurzweil integralgroup characterscomplex Riesz spacezero-dimensional compact abelian group

Mathematics Subject Classification ID

Compact groups (22C05) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Set functions and measures on topological groups or semigroups, Haar measures, invariant measures (28C10) Set functions, measures and integrals with values in ordered spaces (28B15)

Related Items

The \(L^r\)-variational integral ⋮ On descriptive characterizations of an integral recovering a function from its \(L^r\)-derivative ⋮ On the Henstock-Kurzweil integral for Riesz-space-valued functions on time scales ⋮ Reconstruction of a generalized Fourier series from its sum on a compact zero-dimensional group in the non-abelian case ⋮ Unnamed Item ⋮ The 𝐻𝐾ᵣ-integral is not contained in the 𝑃ᵣ-integral

Cites Work

• The Perron integral of order \(k\) in Riesz spaces
• A constructive variant of the definition of an HD-integral
• Une théorie de Denjoy des martingales dyadiques. (A Denjoy theory of dyadic martingales)
• Banach lattices
• Henstock-Kurzweil type integration of Riesz-space-valued functions and applications to Walsh series
• Infinite dimensional analysis. A hitchhiker's guide
• Banach lattices of continuous Banach lattice-valued functions
• The Approximate Symmetric Integral
• Kurzweil-Henstock type integral on zero-dimensional group and some of its applications
• Henstock integration in the plane
• Recent developments in the theory of Haar series
• Integration in Vector Lattices
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