Skip to main content
SpringerLink
Log in

Bases of Exponentials in the Spaces \(L^p ( - \pi ,\pi ) \)

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

It is proved that systems of exponentials orthogonal to measures of a special kind form bases in \(L^p ( - \pi ,\pi ),{\text{ }}1 < p < \infty \), for which an analog of the Riesz theorem on the projection from \(L^p {\text{ onto }}H^p \) is valid.

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. N. Levinson, Gap and Density Theorems, Publ. Amer. Math. Soc., New York, 1940.

    Google Scholar 

  2. A. M. Sedletskii, “Biorthogonal expansions of functions in series of exponentials on intervals of the real axis,” Uspekhi Mat. Nauk [Russian Math. Surveys], 37 (1982), no. 5, 51-95.

    Google Scholar 

  3. A. M. Sedletskii, “On the summability and convergence of nonharmonic Fourier series,” Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.], 64 (2000), no. 3, 151-168.

    Google Scholar 

  4. S. M. Ponomarev, “On an eigenvalue problem,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 249 (1979), no. 5, 1068-1070.

    Google Scholar 

  5. A. Zygmund, Trigonometric Series, vol. 1, Cambridge Univ. Press, Cambridge, 1959.

    Google Scholar 

  6. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Math. Ser., Princeton Univ. Press, Princeton, N.J., 1970.

    Google Scholar 

  7. V. I. Matsaev and M. Z. Solomyak, “On the conditions for the existence of the Stieltjes integral,” Mat. Sb. [Math. USSR-Sb.], 88 (1972), no. 4, 522-535.

    Google Scholar 

  8. A. M. Sedletskii, “On uniform convergence of nonharmonic Fourier series,” Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.], 200 (1991), 299-309.

    Google Scholar 

  9. E. I. Moiseev, “On the basis property of systems of sines and of cosines,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 275 (1984), no. 4, 794-798.

    Google Scholar 

  10. Functional Analysis (S. G. Krein, editor) [in Russian], Nauka, Moscow, 1972.

    Google Scholar 

  11. B. Ya. Levin, The Distribution of Roots of Entire Functions [in Russian], Gostekhizdat, Moscow, 1956.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Russia

    A. M. Sedletskii

Authors
  1. A. M. Sedletskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sedletskii, A.M. Bases of Exponentials in the Spaces \(L^p ( - \pi ,\pi ) \) . Mathematical Notes 72, 383–397 (2002). https://doi.org/10.1023/A:1020555522378

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020555522378

Search

Navigation