Skip to main content
SpringerLink
Log in

The Basis Properties of Some Systems of Exponential Functions, Cosines, and Sines

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We consider some systems of exponential functions, cosines, and sines with complex-valued coefficients and establish a necessary and sufficient condition for completeness and minimality of these systems in Lebesgue spaces.

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. Paley R. and Wiener N., Fourier Transforms in the Complex Domain [Russian translation], Nauka, Moscow (1964).

    Google Scholar 

  2. Levin B. Ya., Distribution of Roots of Entire Functions [in Russian], Gostekhizdat, Moscow (1956).

    Google Scholar 

  3. Sedletski \(\imath \) A. M., “Biorthogonal decompositions of functions in series of exponentials on the intervals of a real axis,” Uspekhi Mat. Nauk, 37,No. 5, 51-95 (1982).

  4. Sedletski \(\imath \) A. M., “On convergence of nonharmonic Fourier series on systems of exponential functions, cosines, and sines,” Dokl. Akad. Nauk SSSR, 301,No. 5, 1053-1056 (1988).

  5. Moiseev E. I., “On the basis property of systems of cosines and sines,” Dokl. Akad. Nauk SSSR, 275,No. 4, 794-798 (1984).

    Google Scholar 

  6. Devdariani G. G., The Basis Property of Some Special Systems of Eigenfunctions of Nonselfadjoint Differential Operators [in Russian], Dis. Kand. Fiz.-Mat. Nauk, Moscow Univ., Moscow (1986).

    Google Scholar 

  7. Bilalov B. T., “On the basis property of some systems of exponential functions, cosines, and sines,” Differentsial'nye Uravneniya, 26,No. 1, 10-16 (1990).

    Google Scholar 

  8. Barmenkov A. N., On the Approximation Properties of Some Systems of Functions [in Russian], Dis. Kand. Fiz.-Mat. Nauk, Moscow Univ., Moscow (1983).

    Google Scholar 

  9. Bilalov B. T., “Necessary and sufficient conditions of the completeness and minimality of the system of the form {A(t)ϕ n(t); B(t)\(\bar \varphi \)n(t)},” Dokl. Ross. Akad. Nauk, 322,No. 6, 1019-1021 (1992).

    Google Scholar 

  10. Danilyuk I. I., Lectures on the Boundary Value Problems for Analytic Functions and Singular Integral Equations [in Russian], Novosibirsk Univ., Novosibirsk (1964).

    Google Scholar 

Download references

Authors
  1. B. T. Bilalov
    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

Bilalov, B.T. The Basis Properties of Some Systems of Exponential Functions, Cosines, and Sines. Siberian Mathematical Journal 45, 214–221 (2004). https://doi.org/10.1023/B:SIMJ.0000021278.64966.d7

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:SIMJ.0000021278.64966.d7

Search

Navigation