Bitangential Interpolation in Generalized Schur Classes

• Published in: Complex analysis and operator theory Vol. 4; no. 4; pp. 701 - 765
• Main Authors: Derkach, Vladimir, Dym, Harry
• Format: Journal Article
• Language: English
• Published: Basel SP Birkhäuser Verlag Basel 01-11-2010
• Subjects: Analysis; Mathematics; Mathematics and Statistics; Operator Theory; Secondary 46C20; 47A48; Kreĭn–Langer factorization; Linear fractional transformation; Coprime factorization; Bitangential interpolation; Resolvent matrix; Primary 30E05; Generalized Schur class; 47B50
• ISSN: 1661-8254; 1661-8262
• DOI: 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 Derkach and Dym (On linear fractional transformations associated with generalized
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-inner matrix functions. Integ Eq Oper Th (2009, in press) arXiv:0901.0193).