Abstract
In this chapter we consider rational matrix functions U(z) which have J-unitary values on the imaginary axis, i.e. (U(z))*JU(z) = J for any regular point z of U in i ℝ. Here J is a signature matrix, namely J = J* and J 2 = I. For this class of matrix functions we analyze the null-pole structure, the special properties of realizations for this class, and the appropriate interpolation problems. We also consider here the interpolation problem with standard local data and its derivatives. These problems are also matricially homogeneous, with the understanding that one is permitted to multiply by J-unitary matrices. The coupling matrix which appeared in the general interpolation problems from Chapter 4 now is Hermitian and plays an extra role. The case J = I hasspecial features and is discussed separately.
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Notes for Part I
D. Alpay and I. Gohberg [ 1988 ], Unitary rational matrix functions, in Operator Theory: Advances and Applications, OT 33, Birkhäuser-Verlag, Basel, pp. 175–222.
J.A. Ball and A.C.M. Ran [ 1987a ], Local inverse spectral problems for rational matrix functions, Integral Equations and Operator Theory 10, 349–415.
J.A. Ball and A.C.M. Ran [ 1987b ], Global inverse spectral problems for rational matrix functions, Linear Algebra and its Applications 86, 237–382.
V.M. Brodskii, I. Gohberg and M.G. Krein [ 1970 ], The definition and basic properties of the characteristic function of a knot, Funkt. Anal. i Prilozh. 1, 88–90.
B. Sz.-Nagy and C. Foias [ 1970 ], Harmonic Analysis of Operators on Hilvert Space, American Elsevier, New York.
L.A. Sakhnovich [ 1986 ], Factorization problems and operator identities, Russian Math. Surveys 41, 1–64.
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Ball, J.A., Gohberg, I., Rodman, L. (1990). Rational Matrix Functions with J-Unitary Values on the Imaginary Line. 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_7
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DOI: https://doi.org/10.1007/978-3-0348-7709-1_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7711-4
Online ISBN: 978-3-0348-7709-1
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