On degenerate interpolation, entropy and extremal problems for matrix Schur functions | Zendy

Vladimir Bolotnikov | Zendy; Harry Dym | Zendy

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On degenerate interpolation, entropy and extremal problems for matrix Schur functions

Author(s) -

Vladimir Bolotnikov,

Harry Dym

Publication year - 1998

Publication title -

integral equations and operator theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.121

H-Index - 48

eISSN - 1420-8989

pISSN - 0378-620X

DOI - 10.1007/bf01194989

Subject(s) - mathematics , degenerate energy levels , positive definite matrix , matrix (chemical analysis) , pure mathematics , entropy (arrow of time) , interpolation (computer graphics) , extension (predicate logic) , mathematical analysis , animation , eigenvalues and eigenvectors , materials science , physics , computer graphics (images) , composite material , programming language , quantum mechanics , computer science

We consider a general bitangential interpolation problem for matrix Schur functions and focus mainly on the case when the associated Pick matrix is singular (and positive semidefinite). Descriptions of the set of all solutions are given in terms of special linear fractional transformations which are obtained using two quite different approaches. As applications of the obtained results we consider the maximum entropy and the maximum determinant extension problems suitably adapted to the degenerate situation.

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