Bitangential interpolation in generalized Schur classes

Mathematics – Classical Analysis and ODEs

Scientific paper

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Second version, corrected typos, changed subsection 5.6, 47 pages

Scientific paper

10.1007/s11785-009-0031-3

Bitangential interpolation problems in the class of matrix valued functions in the generalized Schur class are considered in both the open unit disc and the open right half plane, including problems in which the solutions is not assumed to be holomorphic at the interpolation points. Linear fractional representations of the set of solutions to these problems are presented for invertible and singular Hermitian Pick matrices. These representations make use of a description of the ranges of linear fractional transformations with suitably chosen domains that was developed in a previous paper.

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