# Article

 Title: Kurzweil-Henstock type integral on zero-dimensional group and some of its applications  (English) Author: Skvortsov, Valentin Author: Tulone, Francesco Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 Volume: 58 Issue: 4 Year: 2008 Pages: 1167-1183 Summary lang: English . Category: math . Summary: A Kurzweil-Henstock type integral on a zero-dimensional abelian group is used to recover by generalized Fourier formulas the coefficients of the series with respect to the characters of such groups, in the compact case, and to obtain an inversion formula for multiplicative integral transforms, in the locally compact case. Keyword: Kurzweil-Henstock integral Keyword: derivation basis Keyword: locally compact zero-dimensional abelian group Keyword: characters of a group Keyword: multiplicative integral transform Keyword: inversion formula. MSC: 26A39 MSC: 42C10 MSC: 43A25 idZBL: Zbl 1174.26007 idMR: MR2471174 . Date available: 2010-07-21T08:14:14Z Last updated: 2012-05-31 Stable URL: http://hdl.handle.net/10338.dmlcz/140448 . Reference: [1] Agaev, G. N., Vilenkin, N. Ya., Dzhafarli, G. M., Rubistein, A. I.: Multiplicative system of functions and harmonic analysis on zero-dimensional groups.Baku (1981), Russian. Reference: [2] Golubov, B., Efimov, A., Skvortsov, V.: Walsh Series and Transforms: Theory and Applications.Kluwer Academic Publishers (1991). Zbl 0785.42010, MR 1155844 Reference: [3] Guzman, M. de: Differentiation of Integral in $\mathbb R^n$.Springer-Verlag, Berlin (1975). MR 0457661 Reference: [4] Lee, P. Y., Výborný, R.: The Integral: An Easy Approach after Kurzweil and Henstock.Austral. Math. Soc. Lectures Series 14, University Press, Cambridge (2000). MR 1756319 Reference: [5] Ostaszewski, K. M.: Henstock integration in the plane.Memoirs of the AMS, Providence 63 (1986). Zbl 0596.26005, MR 0856159 Reference: [6] Skvortsov, V. A., Tulone, F.: Henstock type integral in harmonic analysis on zero-dimensional groups.J. Math. Anal. Appl. 322 (2006), 621-628. Zbl 1129.43300, MR 2250603 Reference: [7] Skvortsov, V. A., Tulone, F.: $\mathcal P$-adic Henstock integral in the theory of series with respect to characters of zero-dimensional groups.Vestnik Moskov. Gos. Univ. Ser. Mat. Mekh. 1 (2006), 25-29 Engl. transl. Moscow Univ. Math. Bull. 61 (2006), 27-31. MR 2255051 Reference: [8] Thomson, B. S.: Derivation bases on the real line.Real Anal. Exchange 8 (1982/83), 67-207 and 278-442. Reference: [9] Thomson, B. S.: Derivates of interval functions.Memoirs of the AMS, Providence 93 (1991). Zbl 0734.26003, MR 1078198 .

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