Skip to main content
SpringerLink
Log in

On the divergence of lacunary partial sums of orthogonal series with uniformly bounded functions

  • Published:
Acta Scientiarum Mathematicarum Aims and scope Submit manuscript

Abstract

We verify that in a divergence theorem proved by L. Csernyák and the author the classical monotone decreasing assumption on the “blocksequence” can be weakened to locally almost monotone condition. Furthermore by means of the new result we improve a theorem pertaining to the divergence of the generalized de la Vallée-Poussin means.

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. L. Csernyák und L. Leindler, Über die Divergenz der Partialsummen von Orthogonalreihen, Acta Sci. Math. (Szeged), 27 (1966), 55–61.

    MathSciNet  MATH  Google Scholar 

  2. W. Feller, An introduction to probability theory and its applications, John Wiley & Sons, Inc., New York, 1950.

    MATH  Google Scholar 

  3. L. Leindler, Über die orthogonalen Polynomsysteme, Acta Sci. Math. (Szeged), 21 (1960), 19–46.

    MathSciNet  MATH  Google Scholar 

  4. L. Leindler, Über die verallgemeinerte de la Vallée-Poussinsche Summierbarkeit allgemeiner Orthogonalreihen, Acta Math. Hungar., 16 (1965), 375–387.

    Article  MathSciNet  Google Scholar 

  5. L. Leindler, On the divergence of partial sums of orthogonal series, Publ. Math. Debrecen, 65/1-2 (2004), 173–177.

    MathSciNet  MATH  Google Scholar 

  6. L. Leindler, Refinement of some necessary conditions, Comment. Math. (Prace Mat.) (2004), 145–154.

    Google Scholar 

  7. L. Leindler, One more refinement of Tandori's fundamental divergence theorem, Acta Sci. Math. (Szeged), to appear.

  8. D. E. Menšov, Sur les séries de fonctions orthogonales, Fundamenta Math., 4 (1923), 82–105.

    Article  Google Scholar 

  9. K. Tandori, Über die orthogonalen Funktionen. I, Acta Sci. Math. (Szeged), 18 (1957), 57–130.

    MathSciNet  MATH  Google Scholar 

  10. K. Tandori, Über die Divergenz der Orthogonalreihen, Publ. Math. (Debrecen), 8 (1961), 291–307.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720, Szeged, Hungary

    László Leindler

Authors
  1. László Leindler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to László Leindler.

Additional information

Communicated by L. Kérchy

Dedicated to my friend, Professor Vilmos Totik on his 60th birthday

Supported by the European Union and co-funded by the European Social Fund under the project “Telemedicine-focused research activities on the field of Mathematics, Informatics and Medical sciences” of project number “TÁMOP-4.2.2.A-11/1/KONV-2012-073”.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Leindler, L. On the divergence of lacunary partial sums of orthogonal series with uniformly bounded functions. ActaSci.Math. 80, 121–127 (2014). https://doi.org/10.14232/actasm-013-287-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.14232/actasm-013-287-z

Key words and phrases

AMS Subject Classification (2000)

Search

Navigation