Skip to main content
SpringerLink
Log in

Explicit almost-periodic factorization for a class of triangular matrix functions

  • Published:
Journal d'Analyse Mathématique Aims and scope

Abstract

The canonical generalized factorization of a class of 2×2 triangular matrix symbols associated to convolution operators on a finite interval is studied. A case is considered in which the non-diagonal entry is an almost-periodic trinomial whose spectrum consists of the point zero and two other points of different signs whose distance is less than 1. Explicit formulas for the factors of such a factorization are obtained.

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. A. Bastos, Y. I. Karlovich, A. F. dos Santos and P. M. Tishin, The corona theorem and the canonical factorization of triangular AP-matrix functions-effective criteria and explicit formulas, J. Math. Anal. Appl. 223 (1998), 523–550

    Article  MATH  MathSciNet  Google Scholar 

  2. M. A. Bastos, Y. I. Karlovich, I. M. Spitkovsky and P. M. Tishin, On a new algorithm for almost periodic factorization, in Recent Progress in Operator Theory (Regensburg, 1995), Birkhäuser, Basel, 1998, pp. 53–74.

    Google Scholar 

  3. A. Böttcher, Y. I. Karlovich and I. M. Spitkovsky, Convolution Operators and Factorization of Almost Periodic Matrix Functions, Birkhäuser-Verlag, Basel, 2002.

    MATH  Google Scholar 

  4. M. C. Câmara and C. Diogo, Invertibility of Toeplitz operators and corona conditions in a strip, J. Math. Anal. Appl., 2006, to appear.

  5. M. C. Câmara, A. F. dos Santos and M. C. Martins, A new approach to factorization of a class of almost-periodic triangular symbols and related Riemann-Hilbert problems, J. Funct. Anal. 235 (2006), 559–592.

    Article  MATH  MathSciNet  Google Scholar 

  6. K. Clancey and I. Gohberg, Factorization of Matrix Functions and Singular Integral Operators, Birkhäuser-Verlag, Basel-Boston, Mass., 1981.

    MATH  Google Scholar 

  7. S. Mikhlin and S. Prossdorf, Singular Integral Operators, Springer-Verlag, Berlin, 1986.

    Google Scholar 

  8. S. T. Naique and A. F. dos Santos, Polynomial almost-periodic solutions for a class of Riemann-Hilbert problems with triangular symbols, J. Funct. Anal. 240 (2006), 226–268.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, Avenida Rovisco Pais, Lisboa, Portugal

    M. C. Câmara

  2. Departamento de Matemática, Universidade dos Açores, Portugal

    M. C. Martins

Authors
  1. M. C. Câmara
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. C. Martins
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. C. Câmara.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Câmara, M.C., Martins, M.C. Explicit almost-periodic factorization for a class of triangular matrix functions. J Anal Math 103, 221–260 (2007). https://doi.org/10.1007/s11854-008-0007-7

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11854-008-0007-7

Keywords

Search

Navigation