Abstract
In this work there is an investigation of a family of invertible (i.e. ) analytic matrix-valued functions () which are -contractive and which have monotonically increasing -forms as . Invariance with respect to of the rank of the matrix is established, and conditions for convergence of are investigated. As a special case a theorem is obtained on the invariance of ranks of limiting radii of Weyl disks, which is fundamentally of significance in the theory of classical problems (the moment problem, the Nevanlinna-Pick problem, the Weyl problem on the number of square-integrable solutions of a system of differential equations, and so forth).Bibliography: 17 titles.
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