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An indicator for Wiener-Hopf integral equations with invertible analytic symbol

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Abstract

For Wiener-Hopf integral equations with an operator or matrix valued kernel and with an invertible symbol which is analytic on the real line and at infinity an indicator is introduced. In general this indicator is a bounded linear operator, but when the kernel is matrix valued and the symbol is rational it is a (possibly non-square) matrix. From the indicator the invertibility properties and Fredholm characteristics of the integral equation can be read off. The class of Wiener-Hopf equations studied here is also described in terms of growth conditions on the derivatives of the kernel.

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References

  1. J.S. Barras, R.W. Brockett: H2-functions and infinite-dimensional realization theory. SIAM J. Control 13 (1975), 221–241.

    Google Scholar 

  2. S. Barnett: Introduction to mathematical control theory. Clarendon Press, Oxford, 1975.

    Google Scholar 

  3. H. Bart, I. Gohberg, M.A. Kaashoek: Minimal factorization of matrix and operator functions. Operator Theory: Advances and Applications, Vol. 1, Birkhaüser Verlag, Boston, 1979.

    Google Scholar 

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

    Google Scholar 

  5. H. Bart, I. Gohberg, M.A. Kaashoek: Convolution equations and linear systems. To appear in: Integral Equations and Operator Theory (preprint available).

  6. P. Fuhrmann: Linear systems and operators in Hilbert space. McGraw-Hill, New York, 1981.

    Google Scholar 

  7. I. Gohberg, M.A. Kaashoek, D.C. Lay: Equivalence, linearization and decomposition of holomorphic operator functions. J. Funct. Anal. 28 (1978), 102–144.

    Google Scholar 

  8. S. Goldberg: Unbounded linear operators. McGraw-Hill, New York, 1966.

    Google Scholar 

  9. E. Hille, R.S. Phillips: Functional analysis and semigroups. Amer. Math. Soc. Coll. Publ., Vol.31, Providence R.I., 1957.

    Google Scholar 

  10. T. Kato: Perturbation theory for linear operators. Springer Berlin-Heidelberg-New York, 1966.

    Google Scholar 

  11. J. Mikusinksi: The Bochner Integral. Academic Press, 1978.

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Authors and Affiliations

  1. Wiskundig Seminarium, Vrije Universiteit, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands

    H. Bart & L. G. Kroon

Authors
  1. H. Bart
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  2. L. G. Kroon
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Bart, H., Kroon, L.G. An indicator for Wiener-Hopf integral equations with invertible analytic symbol. Integr equ oper theory 6, 1–20 (1983). https://doi.org/10.1007/BF01691887

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  • DOI: https://doi.org/10.1007/BF01691887

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