Skip to main content
SpringerLink
Log in

Correction and representation theorems for functions of countably many variables

  • Real Analysis
  • Published:
Journal of Contemporary Mathematical Analysis Aims and scope Submit manuscript

Abstract

Some similarities of the well-known theorems on correction and representation of functions of one and several variables are proved for functions of countably many variables.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. Jessen, “The Theory of Integration in a Space of an Infinite Number of Dimensions”, Acta Math. 63, 249–323 (1934).

    Article  MATH  MathSciNet  Google Scholar 

  2. D. Menschoff. “Sur la Convergence Uniforme des Séries de Fourier”, Mat. Sbornik 11(53), 67–96 (1942).

    Google Scholar 

  3. D. E. Menshov, Selected Works (Factorial, Moscow, 1997).

    Google Scholar 

  4. A.A. Talalyan, R. E. Hovsepyan, “D.E.Menshov’s Theorems on Representation and Their Influence to the Development of Metrical Theory of Functions”, UMN, 47:5 (287), 15–44 (1992).

    MATH  Google Scholar 

  5. D. Menschoff, “Sur la Représentation des Fonctions Mesurables par des Séries Trigonométriques”, Mat. Sbornik, 9(51) (3), 667–692 (1941).

    Google Scholar 

  6. S.V. Konyagin, “On theUncertainty Bounds of Trigonometric Series”, Mat. Zametki 44(6), 770–784 (1988).

    Google Scholar 

  7. A. A. Talalyan, “Trigonometric Series Universal With Respect to Subseries”, Izv. Ac. of Sci. of USSR, Ser. Mat. 27, 621–660 (1963).

    MATH  Google Scholar 

  8. F.G. Harutyunyan, “Some Improvement of Menshov’s Theorem on Correction”, Mat. Zametki 35(1), 31–41 (1984).

    MathSciNet  Google Scholar 

  9. F. G. Harutyunyan, “Representation of Measurable Functions of Many Variables by Multiple Trigonometric Series”, Mat. Sbornik 126(168) (3), 267–285 (1985).

    Google Scholar 

  10. N. N. Kholshchevnikova, “Convergence of Trigonometric Series of Countable Set of Variables”, Fundamentalnie Fiz.-Mat. Problemy i Model. Techniko-Teknolog. Sistem 10, 24–27 (2007).

    Google Scholar 

  11. T. I. Akhobadze, “On Countable-Dimensional Fourier Series”, Soobshch AN Gruz. SSR 122(3), 489–492 (1986).

    MATH  MathSciNet  Google Scholar 

  12. V. I. Bogachov, Principals of Measure Theory 2 (NIC, “Regulyarnaya i khaot. Dinamika”, Moscow, 2003).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State Technological University ”Stankin”, Moscow, Russia

    N. N. Kholshchevnikova

Authors
  1. N. N. Kholshchevnikova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. N. Kholshchevnikova.

Additional information

Original Russian Text © N. N. Kholshchevnikova, 2009, published in Izvestiya NAN Armenii. Matematika, 2009, No. 5, pp. 19–27.

This work was supported by RFFI Project 08-01-00669

About this article

Cite this article

Kholshchevnikova, N.N. Correction and representation theorems for functions of countably many variables. J. Contemp. Mathemat. Anal. 44, 284–289 (2009). https://doi.org/10.3103/S1068362309050021

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068362309050021

MSC2000 numbers

Key words

Search

Navigation