Abstract
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.
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G. N. Agaev, N. Ya. Vilenkin, G. M. Dzhafarli and A. I. Rubistein: Multiplicative system of functions and harmonic analysis on zero-dimensional groups. Baku, 1981. (In Russian.)
B. Golubov, A. Efimov and V. Skvortsov: Walsh Series and Transforms: Theory and Applications. Kluwer Academic Publishers, 1991.
M. de Guzman: Differentiation of Integral in ℝn. Springer-Verlag, Berlin, 1975.
P. Y. Lee and R. Výborný: The Integral: An Easy Approach after Kurzweil and Henstock. Austral. Math. Soc. Lectures Series 14, University Press, Cambridge (2000).
K. M. Ostaszewski: Henstock integration in the plane. Memoirs of the AMS, Providence 63 (1986).
V. A. Skvortsov and F. Tulone: Henstock type integral in harmonic analysis on zero-dimensional groups. J. Math. Anal. Appl. 322 (2006), 621–628.
V. A. Skvortsov and F. Tulone: \( \mathcal{P} \)-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.
B. S. Thomson: Derivation bases on the real line. Real Anal. Exchange 8 (1982/83), 67–207 and 278–442.
B. S. Thomson: Derivates of interval functions. Memoirs of the AMS, Providence 93 (1991).
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Skvortsov, V., Tulone, F. Kurzweil-Henstock type integral on zero-dimensional group and some of its applications. Czech Math J 58, 1167–1183 (2008). https://doi.org/10.1007/s10587-008-0077-9
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DOI: https://doi.org/10.1007/s10587-008-0077-9