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Partial Indices of Small Perturbations of a Degenerate Continuous Matrix Function

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Linear Operators and Matrices

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 130))

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Abstract

If A(t) is a continuous on the unit circle n x n matrix function such that det A(t 0) = 0 for some t 0, |t 0| = 1, and s = (s 1, s 2,…,s n,) is a given vector in Z n, then in any neighborhood of A(t)there exists a rational matrix function with partial indices (s 1, s 2,…,s n).

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References

  1. Clancey, K., Gohberg, I., Factorization of matrix functions and singular integral operators, Birkhauser, Basel 1981.

    MATH  Google Scholar 

  2. Gohberg, I. C., Feldman, I.A., Convolution equations and projection methods for their solutions, Amer. Math. Soc., Providence, R.I. 1974.

    Google Scholar 

  3. Gohberg, I. C., Krein, M. G., Systems of integral equations on a half line with kernels depending on the difference of arguments, Amer. Math. Soc. Transl. (2) 14 (1960), 217–287.

    MathSciNet  Google Scholar 

  4. Hagen, R., Roch, S., Silbermann, B., Spectral theory of approximation methods for convolution equations, Birkhauser, Basel 1995.

    Book  Google Scholar 

  5. Hardy, G. H., Littlewood, J. E., Polya, G., Inequalities,Cambridge University Press, Cambridge 1934.

    Google Scholar 

  6. Lancaster, P., Theory of Matrices, Academic Press, New York and London 1969.

    MATH  Google Scholar 

  7. Litvinchuk, G. S., Spitkovskii, I. M., Factorization of measurable matrix functions, Birkhauser, Basel 1995.

    Google Scholar 

  8. Marshall, A. W., Olkin, I., Inequalities: Theory of majorization and its applications, Academic Press, New York 1979.

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Math. and Comp. Sci., Bar-Ilan University, Ramat-Gan, 52900, Israel

    Israel Feldman & Naum Krupnik

  2. Dept. of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel

    Alexander Markus

Authors
  1. Israel Feldman
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  2. Naum Krupnik
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  3. Alexander Markus
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences Raymond and Beverly Sackler, Faculty of Exact Sciences Tel Aviv University, Ramat Aviv, 69978, Israel

    I. Gohberg

  2. Mathematik, Technische Universität Wien, Wiedner Hauptstrasse 8–10/1411, Wien, 1040, Austria

    H. Langer

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© 2002 Springer Basel AG

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Feldman, I., Krupnik, N., Markus, A. (2002). Partial Indices of Small Perturbations of a Degenerate Continuous Matrix Function. In: Gohberg, I., Langer, H. (eds) Linear Operators and Matrices. Operator Theory: Advances and Applications, vol 130. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8181-4_14

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  • DOI: https://doi.org/10.1007/978-3-0348-8181-4_14

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9467-8

  • Online ISBN: 978-3-0348-8181-4

  • eBook Packages: Springer Book Archive

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