Skip to main content
SpringerLink
Log in

Polynomials orthogonal with sign-sensitive weight

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

We introduce the notion of inner product with sign-sensitive weight and construct systems of nonsymmetrically orthonormalized polynomials. We also study some properties of such polynomials (for example, the properties of Fourier coefficients, quadrature formulas of Gauss type, etc.).

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. E. P. Dolzhenko and E. A. Sevast'yanov, “Sign-sensitive approximations. Space of sign-sensitive weights. Rigidity and freedom of a system,”Dokl. Ross. Akad. Nauk [Russian Math. Dokl.],332, No. 6, 686–689 (1993).

    Google Scholar 

  2. E. P. Dolzhenko and E. A. Sevast'yanov, “Sign-sensitive approximations. Uniqueness and stability,”Dokl. Ross. Akad. Nauk [Russian Math. Dokl.],333, No. 1, 5–7 (1993).

    Google Scholar 

  3. V. F. Babenko, “Nonsymmetrical approximations in space of integrable functions,”Uspekhi Mat. Nauk [Russian Math. Surveys],34, No. 4, 409–420 (1982).

    MATH  MathSciNet  Google Scholar 

  4. P. K. Suetin,Classical Orthogonal Polynomials [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  5. G. Szegö,Orthogonal Polynomials, Rev. ed., Vol. XXIII, Amer. Math. Soc., Colloquium Publ., New York (1959)

    Google Scholar 

  6. I. P. Natanson,Theory of Functions of a Real Variable [in Russian], Nauka, Moscow (1974).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dagestan State University, USSR

    A. -R. K. Ramazanov

Authors
  1. A. -R. K. Ramazanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 59, No. 5, pp. 737–752, May, 1996.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ramazanov, A.R.K. Polynomials orthogonal with sign-sensitive weight. Math Notes 59, 531–542 (1996). https://doi.org/10.1007/BF02308821

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02308821

Keywords

Search

Navigation