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Ball, Joseph A.; Clancey, Kevin F.

An elementary description of partial indices of rational matrix functions. (English) Zbl 0719.47014

Integral Equations Oper. Theory 13, No. 3, 316-322 (1990).
An (unpublished) test of S. Pattanayak for the invertibility of a Toeplitz operator with a rational matrix symbol on the unit circle is extended to arbitrary contours. The generalization leads in a simple manner to an elementary description of the factorization indices of a regular rational matrix function relative to a contour. The formulae for the indices given by the authors differ from the ones in I. Gohberg, L. Lerer and L. Rodman, Bull. Am. Math. Soc. 84, 275-277 (1978; Zbl 0381.30020), but the order of their computational complexity is about the same.
Reviewer: M.A.Kaashoek (Amsterdam)

Cited in 3 Documents

MSC:

47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators

Keywords:

invertibility of a Toeplitz operator with a rational matrix symbol on the unit circle; factorization indices of a regular rational matrix function relative to a contour

Citations:

Zbl 0381.30020
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Full Text: DOI

References:

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