On an operator approach to interpolation problems for Stieltjes functions | Zendy

Vladimir Bolotnikov | Zendy; Lev Sakhnovich | Zendy

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On an operator approach to interpolation problems for Stieltjes functions

Author(s) -

Vladimir Bolotnikov,

Lev Sakhnovich

Publication year - 1999

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/bf01228042

Subject(s) - mathematics , interpolation (computer graphics) , operator (biology) , shift operator , linear fractional transformation , riemann–stieltjes integral , linear map , birkhoff interpolation , linear interpolation , transformation (genetics) , algebra over a field , set (abstract data type) , pure mathematics , mathematical analysis , polynomial interpolation , compact operator , integral equation , extension (predicate logic) , computer graphics (images) , repressor , chemistry , computer science , biochemistry , transcription factor , programming language , animation , gene , robust control , polynomial , quantum mechanics , physics , nonlinear system

A general interpolation problem for operator-valued Stieltjes functions is studied using V. P. Potapov's method of fundamental matrix inequalities and the method of operator identities. The solvability criterion is established and under certain restrictions the set of all solutions is parametrized in terms of a linear fractional transformation. As applications of a general theory, a number of classical and new interpolation problems are considered.

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