Abstract
In this chapter we develop further the results from Chapter 1 for meromorphic matrix valued functions. In addition to null structure, pole structure is introduced and studied. In contrast to the scalar case, a new feature appears in the matrix case, namely, a meromorphic matrix function can have a zero and a pole at the same point. This chapter contains the analysis of null and pole chains, null and pole pairs, null and pole triples and singular parts, as well as connections among them.
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Notes for Part I
I.C. Gohberg and E.I. Sigal [ 1971 ], On operator generalizations of the logarithmic residue theorem and the theorem of Rouché, Math. USSR Sb 13, 603–625.
I. Gohberg and L. Rodman [ 1986 ], Interpolation and local data for meromorphic matrix and operator functions, Integral Equations and Operator Theory 9, 60–94.
H. Bart, I. Gohberg and M.A. Kaashoek [ 1979 ], Minimal Factorization of Matrix and Operator Functions, Birkhäuser-Verlag, Basel.
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© 1990 Springer Basel AG
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Ball, J.A., Gohberg, I., Rodman, L. (1990). Local Data for Meromorphic Matrix Functions. In: Interpolation of Rational Matrix Functions. Operator Theory: Advances and Applications, vol 45. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7709-1_4
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DOI: https://doi.org/10.1007/978-3-0348-7709-1_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7711-4
Online ISBN: 978-3-0348-7709-1
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