Denjoy and P-path integrals on compact groups in an inversion formula for multiplicative transforms

Francesco Tulone

doi:10.2478/v10127-009-0003-z

.blurhash-client-img { display: none !important; }

Denjoy and P-path integrals on compact groups in an inversion formula for multiplicative transforms

Tatra Mountains Mathematical Publications

Volume 42 (2009): Issue 1 (April 2009)

By: Francesco Tulone

Open Access

|Nov 2012

Abstract

Denjoy and P-path Kurzweil-Henstock type integrals are defined on compact subsets of some locally compact zero-dimensional abelian groups. Those integrals are applied to obtain an inversion formula for the multiplicative integral transform.

References

[1] AGAEV, G. N.-VILENKIN, N. YA.-DZHAFARLI, G. M.-RUBISTEIN, A. I.: Multiplicative System of Functions and Harmonic Analysis on Zero-Dimensional Groups. “Ehlm”, Baku, 1981. (In Russian)
Search in Google Scholar
[2] BONGIORNO, B.-DI PIAZZA, L.-SKVORTSOV, V. A.: The Ward property for a P-adic basis and the P-adic integral, J. Math. Anal. Appl. 285 (2003) 578-592.
Search in Google Scholar
[3] GOLUBOV, B.-EFIMOV, A.-SKVORTSOV, V.: Walsh Series and Transforms. Theory and Applications. Math. Appl. (Soviet Ser.), Vol. 64, Kluwer Academic Publishers, Dordrecht, 1991.10.1007/978-94-011-3288-6
Search in Google Scholar
[4] GORDON, R. A.: The Integrals of Lebesgue, Denjoy, Perron, and Henstock Theory, Grad. Stud. Math., Vol. 4, Amer. Math. Soc., Providence, RI, 1994.10.1090/gsm/004
Search in Google Scholar
[5] SKVORTSOV, V. A.-KOROLEVA, M. P.: Series in multiplicative systems convergent to Denjoy-integrable functions, Sb. Math. 186 (1995), No. 12, 1821-1842; translation from Mat. Sb. 186 (1995), No. 12, 129-150.
Search in Google Scholar
[6] SKVORTSOV, V. A.-TULONE, F.: The P-adic Henstock integral in the problem of function representations by multiplicative transforms, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2005 (2005), No. 3, 41-44, translation in Moscow Univ. Math. Bull. 60 (2005), No. 3, 19-22.
Search in Google Scholar
[7] SKVORTSOV, V. A.-TULONE, F.: On the problem of recovering the coefficients of series with respect to characters of zero-dimensional groups, Tatra Mt. Math. Publ. 34 (2006), 307-320.
Search in Google Scholar
[8] SKVORTSOV, V. A.-TULONE, F.: Henstock type integral in harmonic analysis on zero-dimensional groups, J. Math. Anal. Appl. 322 (2006), 621-628.10.1016/j.jmaa.2005.09.053
Search in Google Scholar
[9] SKVORTSOV, V. A.-TULONE, F.: Integration of both the derivatives with respect to P-paths and approximative derivatives, Mat. Zametki 85 (2009), No. 2, 283-291, translation in Math. Notes 85 (2009), 260-266.10.1134/S0001434609010295
Search in Google Scholar
[10] RUDIN, W.: Fourier Analysis on Groups. John Wiley & Sons, New York, 1967.
Search in Google Scholar