Integration of Functions Ranging in Complex Riesz Space and Some Applications in Harmonic Analysis
Matematičeskie zametki, Tome 98 (2015) no. 1, pp. 12-26
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The theory of Henstock–Kurzweil integral is generalized to the case of functions ranging in complex Riesz space $R$ and defined on any zero-dimensional compact Abelian group. The constructed integral is used to solve the problem of recovering the $R$-valued coefficients of series in systems of characters of these groups by using generalized Fourier formulas.
Keywords:
complex Riesz space, zero-dimensional compact Abelian group, group characters, Henstock–Kurzweil integral.
@article{MZM_2015_98_1_a1,
author = {A. Bokkuto and V. A. Skvortsov and F. Tulone},
title = {Integration of {Functions} {Ranging} in {Complex} {Riesz} {Space} and {Some} {Applications} in {Harmonic} {Analysis}},
journal = {Matemati\v{c}eskie zametki},
pages = {12--26},
publisher = {mathdoc},
volume = {98},
number = {1},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2015_98_1_a1/}
}
TY - JOUR AU - A. Bokkuto AU - V. A. Skvortsov AU - F. Tulone TI - Integration of Functions Ranging in Complex Riesz Space and Some Applications in Harmonic Analysis JO - Matematičeskie zametki PY - 2015 SP - 12 EP - 26 VL - 98 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2015_98_1_a1/ LA - ru ID - MZM_2015_98_1_a1 ER -
%0 Journal Article %A A. Bokkuto %A V. A. Skvortsov %A F. Tulone %T Integration of Functions Ranging in Complex Riesz Space and Some Applications in Harmonic Analysis %J Matematičeskie zametki %D 2015 %P 12-26 %V 98 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/MZM_2015_98_1_a1/ %G ru %F MZM_2015_98_1_a1
A. Bokkuto; V. A. Skvortsov; F. Tulone. Integration of Functions Ranging in Complex Riesz Space and Some Applications in Harmonic Analysis. Matematičeskie zametki, Tome 98 (2015) no. 1, pp. 12-26. http://geodesic.mathdoc.fr/item/MZM_2015_98_1_a1/