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On real and “symplectic” meromorphic plus-matrix-functions and corresponding linear fractional transformations. (Russian. English summary) Zbl 1059.47015
Summary: The main result of the present paper is that, if a linear fractional transformation with nondegenerate matrix of coefficients \(A(z)\) meromorphic in the unit disk maps the class of holomorphic contractive matrix functions into itself so that real (symmetric) matrix functions are transformed into real (symmetric) matrix functions, then there exists a meromorphic scalar function \(\rho(z)\), such that \(\rho^{-1}(z)A(z)\) is a \(j\)-expansive real (“symplectic” or “antisymplectic”) matrix function.
47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
30G30 Other generalizations of analytic functions (including abstract-valued functions)