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Spectral Theory of Selfadjoint Wiener-Hopf Operators with Rational Symbols

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Topics in Matrix and Operator Theory

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 50))

Abstract

Explicit formulas for the resolution of the identity of selfadjoint Wiener-Hopf operators with rational matrix symbol are constructed. The formulas are given in terms of a realization of the symbol.

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References

  1. Baumgärtel, H.: Analytic perturbation theory for matrices and operators. Operator Theory: Advances and Applications. Vol. 15, Birkhäuser Verlag (Basel) 1985.

    Google Scholar 

  2. Bart, H., Gohberg, I., Kaashoek, M.A.: Minimal factorization of matrix and operator functions. Operator Theory: Advances and Applications. Vol.1, Birkhäuser Verlag (Basel) 1979.

    Google Scholar 

  3. Bart, H., Gohberg, I., Kaashoek, M.A.: Wiener-Hopf integral equations, Toeplitz matrices and linear systems. In Toeplitz Centennial (ed. I. Gohberg), Operator Theory: Advances and Applications. Vol.4, Birkhäuser Verlag (Basel) 1982, 85-135.

    Google Scholar 

  4. Bachman, G., Narici, L.: Functional analysis. Academic Press (New York, etc.) 1966.

    Google Scholar 

  5. Conway, J.B.: Functions of one complex variable. Springer-Verlag, New York, 1978.

    Book  Google Scholar 

  6. Dunford, N., Schwartz, J.T.: Linear operators, part II: Spectral theory. New York: Interscience Publishers 1963.

    Google Scholar 

  7. Gohberg, I., Lancaster, P., Rodman, R.: Matrices and indefinite scalar products. Operator Theory: Advances and Applications. Vol.8, Birkhäuser Verlag (Basel) 1983.

    Google Scholar 

  8. Gohberg, I., Lancaster, P., Rodman, R.: Matrix polynomials. Academic Press (New York, etc.) 1982.

    Google Scholar 

  9. Gohberg, I., Lancaster, P., Rodman, R.: Invariant subspaces of matrices with applications. Canadian mathematical society of monographs and advanced texts, John Wiley and Sons. New York, etc., 1986.

    Google Scholar 

  10. Hartman, P., Wintner, A.: The spectra of Toeplitz matrices. Amer. Journal of Math., 76 (1954), 867–882.

    Article  Google Scholar 

  11. Iohvidov, I., Krein, M.G., Langer, H.: Introduction to spectral theory of operators in spaces with an indefinite metric. Math. Research, Vol. 9, Akademie-Verlag, Berlin, 1982.

    Google Scholar 

  12. Kato, T.: Perturbation theory for linear operators. Springer-Verlag, Berlin, 1966.

    Book  Google Scholar 

  13. Kailath, T.: Linear systems. Prentice-Hall, Englewood Cliffs, NJ, 1980.

    Google Scholar 

  14. Ran, A.C.M.: Minimal factorization of selfadjoint rational matrix functions. Integral Equations and Operator Theory, 5 (1982), 850–869.

    Article  Google Scholar 

  15. Rodman, L.: On the structure of selfadjoint Toeplitz operators with rational symbol. Proc. Amer. Math. Soc., Vol. 92 (1984), 487–494.

    Article  Google Scholar 

  16. Rosenblum, M.: Selfadjoint Toeplitz operators and associated orthonormal functions. Proc. Amer. Math. Soc., Vol. 13 (1962), 590–595.

    Article  Google Scholar 

  17. Rosenblum, M.: The absolute contonuity of Toeplitz matrices. Pacific J.Math. 10 (1960), 987–996.

    Article  Google Scholar 

  18. Rosenblum, M.: A concrete spectral theory for selfadjoint Toeplitz operators. Amer. J. Math. 87 (1965), 709–718.

    Article  Google Scholar 

  19. Rudin, W.: Real and complex analysis, third edition. McGraw-Hill Book Company, New York, etc., 1986.

    Google Scholar 

  20. Rosenblum, M., Rovnyak, J.: Hardy classes and operator theory. Oxford mathematical monographs, Oxford Unversity Press, New York, etc., 1985.

    Google Scholar 

  21. Taylor, A.E.: Introduction to functional analysis. John Wiley and Sons. New York, etc., 1958.

    Google Scholar 

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© 1991 Springer Basel AG

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Vreugdenhil, R. (1991). Spectral Theory of Selfadjoint Wiener-Hopf Operators with Rational Symbols. In: Bart, H., Gohberg, I., Kaashoek, M.A. (eds) Topics in Matrix and Operator Theory. Operator Theory: Advances and Applications, vol 50. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5672-0_15

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  • DOI: https://doi.org/10.1007/978-3-0348-5672-0_15

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5674-4

  • Online ISBN: 978-3-0348-5672-0

  • eBook Packages: Springer Book Archive

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