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Mat. Sb., 2007, Volume 198, Number 7, Pages 63–90 (Mi msb1506)  

This article is cited in 4 scientific papers (total in 4 papers)

Several properties of generalized multivariate integrals and theorems of the du Bois-Reymond type for Haar series

M. G. Plotnikov

Vologda State Academy of Milk Industry

Abstract: Several properties of generalized multivariate integrals are considered. In the two-dimensional case the consistency of the regular Perron integral is proved, as well as the consistency of a generalized integral solving the problem of the recovery of the coefficients of double Haar series in a certain class. Several generalizations of Skvortsov's well-known theorem are obtained as consequences, for instance, the following result: if a double Haar series converges for some $\rho\in(0,1/2]$ $\rho$-regularly everywhere in the unit square to a finite function that is Perron-integrable in the $\rho$-regular sense, then the series in question is the Fourier–Perron series of its sum.
Bibliography: 20 titles.

DOI: https://doi.org/10.4213/sm1506

Full text: PDF file (711 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2007, 198:7, 967–991

Bibliographic databases:

UDC: 517.518.36+517.518.126
MSC: 26B15, 42B05
Received: 26.01.2006 and 03.04.2007

Citation: M. G. Plotnikov, “Several properties of generalized multivariate integrals and theorems of the du Bois-Reymond type for Haar series”, Mat. Sb., 198:7 (2007), 63–90; Sb. Math., 198:7 (2007), 967–991

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. G. Plotnikov, “Generalized Riemann-Type Integrals on the Plane and an Example of Double Haar Series”, Math. Notes, 86:4 (2009), 567–576  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. M. G. Plotnikov, Yu. A. Plotnikova, “Martingaly i teoremy Kantora–Yunga–Bernshteina i Valle-Pussena”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:4(2) (2014), 569–574  mathnet  crossref  elib
    3. Skvortsov V. Tulone F., “Multidimensional Dyadic Kurzweil-Henstock- and Perron-Type Integrals in the Theory of Haar and Walsh Series”, J. Math. Anal. Appl., 421:2 (2015), 1502–1518  crossref  mathscinet  zmath  isi  elib  scopus
    4. Tulone F., Skvortsov V., “Multidimensional P-Adic Integrals in Some Problems of Harmonic Analysis”, Minimax Theory Appl., 2:1, SI (2017), 153–174  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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