Skip to main content
SpringerLink
Log in

Factorization in the Wiener algebra of a class of 2×2 matrix functions

  • Published:
Integral Equations and Operator Theory Aims and scope Submit manuscript

Abstract

In this paper the problem of the factorization in the Wiener algebra of a class of 2×2 matrix functions of Daniele type is considered. For these matrix functions necessary and sufficient conditions for the existence of a canonical factorization are obtained and, provided these conditions are fulfilled, the factors of such factorization can be derived in an explicit form.

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. Clancey, K. and Gohberg, I.: Factorization of Matrix Functions and Singular Integral Operators. Operator Theory: Advances and Applications, vol. 3, Birkhäuser Verlag, Basel, etc., 1981.

    Google Scholar 

  2. Daniele, V. T.: On the factorization of Wiener-Hopf matrices in problems solvable with Hurd's method. I.E.E.E. Trans. Antennas Propag., vol. AP-26 (1978), 614–616.

    Google Scholar 

  3. Daniele, V. T.: On the solution of two coupled Wiener-Hopf equations, SIAM J. Appl. Math., vol. 44, No. 4 (1984), 667–680.

    Google Scholar 

  4. dos Santos, A. F., Lebre, A. B. and Teixeira, F. S.: The diffraction problem for a half plane with different face impedances revisited, J. Math. Anal. and Appl., to appear.

  5. Gohberg, I. and Krein, M. G.: Systems of integral equations on a half line with kernels depending on the difference of arguments. Uspehi Mat. Nauk. 13, No. 2 (80), 3–72 (1958). English Translation: Amer. Math. Soc. Trans. (2) 14, 217–287 (1960).

    Google Scholar 

  6. Hurd, R. A.: The explicit factorization of 2×2 Wiener-Hopf matrices, Preprint Nr. 1040 Fachbereich Mathematik, Technische Hochschule Darmstadt, 1987.

  7. Khrapkov, A. A.: Certain cases of the elastic equilibrium of an infinite wedge with a non-symmetric notch at the vertex, subjected to the concentrated force. Prikl. Mat. Mekch., 35 (1971), 625–637.

    Google Scholar 

  8. Meister, E. and Speck, F.-O.: Wiener-Hopf factorization of certain nonrational matrix functions in Mathematical Physics, Preprint Nr. 1156 Fachbereich Mathematik, Technische Hochschule Darmstadt, 1988.

  9. Nashed, M. Z. and Votruba, G. F.: A unified operator theory of generalized inverses, in: Generalized Inverses and Applications (ed. M. Z. Nashed), Academic Press, 1976.

  10. Rawlins, A. D.: A note on the factorization of matrices occuring in Wiener-Hopf problems, I.E.E.E. Trans. Antennas Propag., vol. AP-28 (1980), 933–934.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departmento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1096, Lisboa Codex, Portugal

    A. B. Lebre

  2. Centro de Análise e Processamento de Sinais Complexo I do I.N.I.C., Av. Rovisco Pais, 1000, Lisboa, Portugal

    A. B. Lebre

Authors
  1. A. B. Lebre
    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

Lebre, A.B. Factorization in the Wiener algebra of a class of 2×2 matrix functions. Integr equ oper theory 12, 408–423 (1989). https://doi.org/10.1007/BF01235740

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01235740

Keywords

Search

Navigation