Advertisement

Factorization Algorithm for Some Special Matrix Functions

  • Ana C. Conceição
  • Viktor G. Kravchenko
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 181)

Abstract

We will see that it is possible to construct an algorithm that allows us to determine an effective factorization of some matrix functions. For those matrix functions it is shown that its explicit factorization can be obtained through the solutions of two non-homogeneous equations.

Keywords

Explicit factorization algorithm singular integral operator nonhomogeneous equations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    H. Bart, I. Gohberg, and M.A. Kaashoek, Minimal Factorization of Matrix and Operator Functions, Operator Theory: Advances and Applications 1, Birkhäuser Verlag, Basel-Boston, 1979.Google Scholar
  2. [2]
    K. Clancey and I. Gohberg, Factorization of Matrix Functions and Singular Integral Operators, Operator Theory: Advances and Applications 3, Birkhäuser Verlag, Basel-Boston, 1981.Google Scholar
  3. [3]
    A.C. Conceição and V.G. Kravchenko, About explicit factorization of some classes of non-rational matrix functions, to appear in Mathematische Nachrichten 280, No. 9–10, (2007), 1022–1034.Google Scholar
  4. [4]
    A.C. Conceição, V.G. Kravchenko, and F.S. Teixeira, Factorization of matrix functions and the resolvents of certain operators, in Operator Theory: Advances and Applications, Birkhäuser Verlag 142 (2003), 91–100.Google Scholar
  5. [5]
    A.C. Conceição, V.G. Kravchenko, and F.S. Teixeira, Factorization of some classes of matrix functions and the resolvent of a Hankel operator, in Factorization, Singular Operators and Related Problems, Kluwer Academic Publishers (2003), 101–110.Google Scholar
  6. [6]
    T. Ehrhardt, and F.-O. Speck, Transformation techniques towards the factorization of non-rational 2×2 matrix functions, Linear Algebra and its applications 353 (2002), 53–90.CrossRefMathSciNetzbMATHGoogle Scholar
  7. [7]
    L.D. Faddeev and L.A. Takhtayan, Hamiltonian Methods in the Theory of Solitons, Springer-Verlag, Berlin, 1987.zbMATHGoogle Scholar
  8. [8]
    I. Feldman, I. Gohberg, and N. Krupnik, An Explicit Factorization Algorithm, Integral Equations and Operator Theory, Birkhäuser Verlag, Basel 49 ( 2004), 149–164.Google Scholar
  9. [9]
    V.G. Kravchenko and A.I. Migdal’skii, A regularization algorithm for some boundary-value problems of linear conjugation (English), Dokl. Math. 52 (1995), 319–321.zbMATHGoogle Scholar
  10. [10]
    G.S. Litvinchuk, Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift, Mathematics and its Applications 523, Kluwer Academic Publishers, Dordrecht, 2000.Google Scholar
  11. [11]
    G.S. Litvinchuk and I.M. Spitkovskii, Factorization of Measurable Matrix Functions, Operator Theory: Advances and Applications 25, Birkhäuser Verlag, Basel, 1987.Google Scholar
  12. [12]
    S. Prössdorf, Some Classes of Singular Equations, North-Holland, Amsterdam, 1978.zbMATHGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Ana C. Conceição
    • 1
  • Viktor G. Kravchenko
    • 1
  1. 1.Área Dep. de MatemáticaUniversidade do AlgarveFaroPortugal

Personalised recommendations