Linear Operators and Matrices pp 185-195 | Cite as
Partial Indices of Small Perturbations of a Degenerate Continuous Matrix Function
Conference paper
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).
Keywords
Unit Circle Small Perturbation Matrix Function Toeplitz Operator Convolution Equation
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References
- [1]Clancey, K., Gohberg, I., Factorization of matrix functions and singular integral operators, Birkhauser, Basel 1981.MATHGoogle 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.MathSciNetGoogle Scholar
- [4]Hagen, R., Roch, S., Silbermann, B., Spectral theory of approximation methods for convolution equations, Birkhauser, Basel 1995.CrossRefGoogle 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.MATHGoogle 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.MATHGoogle Scholar
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