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Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations by Harry Dym, Damir Z. Arov

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4Interpolation problems, resolvent matrices and de Branges spaces

This chapter is devoted to the interplay between

(1) three interpolation problems;

(2) descriptions of their solutions as linear fractional transformations (of Schur class mvf’s) based on appropriately restricted resolvent matrices when the interpolation problems are completely indeterminate; and

(3) formulas for these resolvent matrices in terms of the given data when the interpolation problems are strictly completely indeterminate.

The basic fact is that there is a one-to-one correspondence between completely indeterminate interpolation problems and appropriately restricted resolvent matrices. More precisely:

The abbreviations in the first column stand for generalized Caratheodory ...

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