Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 20, No. 2, pp. 207-224 (2004)

Henstock-Kurzweil type integrals in P-adic harmonic analysis

V. Skvortsov

Moscow State University, Akademia Bydgoska im. Kazimierza Wielkiego

Abstract: Some recent results related to the P-adic derivatives and integrals are surveyed. Applications of the Henstock-Kurzweil P-integral and the Perron P-integral to the problem of recovering the coefficients of series with respect to the Vilenkin system and the Haar system (both in one dimension and in higher dimensions) are discussed. The case of the continual analogue of the Vilenkin system is also considered.

Keywords: Henstock-Kurzweil integral, Perron integral, $\mathcal P$-adic derivate basis, variational measure, Walsh system, Vilenkin system, Haar system.

Classification (MSC2000): 26A39

Full text of the article:

[Previous Article] [Next Article] [Contents of this Number]
© 2004 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition