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On some properties of factorization indices

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Abstract

Various kinds of factorization indices are considered (right partial indices, left partial indices, Birkhoff indices), and some connections between them are described. We solve also the problem on the relation between the partial indices of two matrix functions and of their product.

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References

  1. G. D. Birkhoff,A theorem on matrices of analytic functions, Math. Ann.74 (1913), 122–133.

    Google Scholar 

  2. I. S. Čebotaru,The reduction of systems of Wiener-Hopf equations to systems with vanishing indices, Bull. Acad. Shtiince RSS Moldov. N 8 (1967), 54–66. (Russian)

    Google Scholar 

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

    Google Scholar 

  4. I. Feldman, I. Gohberg and N. Krupnik,On explicit factorization and application, Integral Equations and Operator Theory21 (1995), 430–459.

    Google Scholar 

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

    Google Scholar 

  6. I. C. Gohberg and M. G. Krein,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.

    Google Scholar 

  7. I. Gohberg, P. Lancaster and L. Rodman,Invariant subspaces of matrices and applications, Wiley, New-York, 1986.

    Google Scholar 

  8. R. Hagen, S. Roch and B. Silbermann,Spectral theory of approximation methods for convolution equations, Birkhäuser, Basel, 1995.

    Google Scholar 

  9. G. H. Hardy, J. E. Littlwood, G. Polya,Inequalities, Cambridge University Press, Cambridge, 1934.

    Google Scholar 

  10. G. S. Litvinchuk and I. M. Spitkovskii,Factorisation of measurable matrix functions, Birkhäuser, Basel, 1987.

    Google Scholar 

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

    Google Scholar 

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Dedicated to the memory of Mark Grigorievich Krein

This research was supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities.

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Feldman, I., Markus, A. On some properties of factorization indices. Integr equ oper theory 30, 326–337 (1998). https://doi.org/10.1007/BF01195587

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  • DOI: https://doi.org/10.1007/BF01195587

MSC 1991

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