Skip to main content
Log in

Generalized factorization for a class ofn×n matrix functions — Partial indices and explicit formulas

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

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

The generalized factorization of a class of continuous non-rationaln×n matrix-functions is studied. The partial indices are determined and, in the case of existence of a canonical factorization, explicit formulas for the factors are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ahlfors, L.: Complex analysis; Mc-Graw Hill, 1979, 3rd ed.

  2. Câmara, M. C., Lebre, A. B. and Speck, F.-O.: Generalized factorization for a class of Jones form matrix functions; accepted for publication in Proc. R. Soc. Edinburgh. 1992.

  3. Carleman, J.: L'intégrale de Fourier et questions qui s'y rattachent, Uppsala, Almquist & Wiksells, 1944.

    Google Scholar 

  4. Clancey K. and Gohberg, I.: Factorization of matrix functions and singular integral operators; Birkhäuser, Basel, 1981.

    Google Scholar 

  5. Daniele, V. G.: On the solution of two coupled Wiener-Hopf equations; SIAM J. Appl. Math., 44 (1984), 667–680.

    Google Scholar 

  6. Duduchava, R.: Integral equations in convolution with discontinuous pre-symbols, Leipzig, 1979.

  7. Duren, P.: Theory ofH p spaces, Academic Press, 1970.

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

  9. Jones, D. S.: Commutative Wiener-Hopf factorization of a matrix. Proc. R. Soc. London A 393 (1984), 185–192.

    Google Scholar 

  10. Jörgens, K.: Linear integral operators, Pitman, 1982.

  11. Koosis, P.: Introduction toH p spaces, London Mathematical Society Lecture Notes Series 40, Cambridge University Press, 1980.

  12. Lebre, A. B.: Factorization in the Wiener algebra of a class of 2×2 matrix functions, Int. Eq. and Op. Th., 12 (1989), 408–423.

    Google Scholar 

  13. Lebre, A. B.: A note on the reduction of Jones-formn×n matrix functions to a special form, Manuscript.

  14. Lebre, A. B., dos Santos, A. F.: Generalized factorization for a class of non-rational 2×2 matrix functions; Int. Eq. and Op. Th., 13 (1990) 671–700.

    Google Scholar 

  15. Meister, E. Penzel, F.: On the reduction of the factorization of matrix functions of Daniele-Khrapkov type to a scalar boundary value problem on a Riemann surface, Preprint 1351, 1991, Fachbereich Mathematik, Technische Hochschule, Darmstadt.

    Google Scholar 

  16. Mikhlin, S. G. and Prössdorf, S.: Singular integral operators, Springer; Berlin 1986 (in German, 1980).

    Google Scholar 

  17. Moiseev, N. G.: On factorization of matrix-valued functions of special form, Soviet Math. Dokl. vol. 39 (1989), no 2, 264–267.

    Google Scholar 

  18. Okikiolu, G. O.: Aspects of the theory of bounded integral operators inL p-spaces, Academic Press, 1971.

  19. Prössdorf, S., Speck, F.-O.: A factorization procedure for 2×2 matrix functions on the circle with two rationally independent entries; Proc. R. Soc. Edinburgh, 115 A (1990) 119–138.

    Google Scholar 

  20. Riesz, M.: Sur les fonctions conjuguées, Math. Z., vol. 27 (1927), 218–244.

    Google Scholar 

  21. Rudin, W.: Real and complex analysis, 2nded., Mc Graw-Hill.

  22. Teixeira, F.: Generalized factorization for a class of symbols in\([PC(\mathop \mathbb{R}\limits^ \cdot )]_{2 \times 2} \), Appl. Anal., 36 (1990), 95–117.

    Google Scholar 

  23. Widom, H.: Singular integral equations inL p , Trans. Amer. Math. Soc., 97 (1960), 131–160.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Câmara, M.C., dos Santos, A.F. Generalized factorization for a class ofn×n matrix functions — Partial indices and explicit formulas. Integr equ oper theory 20, 198–230 (1994). https://doi.org/10.1007/BF01679671

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01679671

AMS

Navigation