Henstock-Kurzweil type integration of Riesz-space-valued functions and applications to Walsh series. (English) Zbl 1067.28009

Boccuto, A.; Skvortsov, V. A.

Real Anal. Exch. 29(2003-2004), No. 1, 419-438 (2004).

From the Introduction: “Some versions of Henstock-Kurzweil integral with respect to different derivation bases for functions with values in Dedekind complete Riesz spaces are studied. Considering a wide class of Riesz spaces the authors prove for this type of Henstock-Kurzweil integrals some versions of the fundamental theorem of integral calculus. In a particular case of the dyadic basis this theorem is applied to the problem of recovering the coefficients of Walsh series from their sums by generalized Fourier formulas in which integrals are understood in the above sense.”

Reviewer: Boris I. Golubov (Dolgoprudny)

MSC:

28B05	Vector-valued set functions, measures and integrals
28B15	Set functions, measures and integrals with values in ordered spaces
26A39	Denjoy and Perron integrals, other special integrals
42C10	Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
42C25	Uniqueness and localization for orthogonal series
46G10	Vector-valued measures and integration

Keywords:

Riesz spaces; Henstock-Kurzweil integration; derivation basis; fundamental theorem of calculus; interval functions; Walsh series