Skip to main content
SpringerLink
Log in

Investigating the Orthogonality Conditions of Wavelets Based on Jacobi Polynomials

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The properties of wavelets based on Jacobi polynomials are analyzed. The conditions are considered under which these wavelets are mutually orthogonal and under which the wavelet basis is characterized by a minimum Riesz ratio. These problems lead to the solution of systems of nonlinear equations by a method proposed earlier by the authors.

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. M. Unser and A. Aldroubi, Wavelets: Mathematics and Applications, CRC Press, Boca Raton (1994).

    MATH  Google Scholar 

  2. B. Fischer and J. Prestin, “Wavelets based on orthogonal polynomials,” Mathematics of Computation, Vol. 66, 1593–1618 (1997).

  3. T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York–London–Paris (1978).

    MATH  Google Scholar 

  4. V. Yu. Semenov, “A method to find all the roots of the system of nonlinear algebraic equations based on the Krawczyk operator,” Cybernetics and Systems Analysis, Vol. 51, No. 5, 819–825 (2015).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DELTA SPE Scientific and Production Enterprise, Kyiv, Ukraine

    V. Semenov

  2. Institute of Mathematics of the University of Lubeck, Lubeck, Germany

    J. Prestin

Authors
  1. V. Semenov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Prestin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Semenov.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2018, pp. 182–190.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Semenov, V., Prestin, J. Investigating the Orthogonality Conditions of Wavelets Based on Jacobi Polynomials. Cybern Syst Anal 54, 678–686 (2018). https://doi.org/10.1007/s10559-018-0069-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-018-0069-1

Keywords

Search

Navigation