An Abstract Interpolation Problem and the Extension Theory of Hermitian Operators

Details An Abstract Interpolation Problem and the Extension Theory of Hermitian Operators An Abstract Interpolation Problem and the Extension Theory of Hermitian Operators

2007-06-13

arxiv.org/abs/0706.1896v1

Topics in Interpolation Theory. Operator Theory: advances and Applications, Vol. 95. Birkhauser, 1997

Mathematics

Functional Analysis

Scientific paper

The algebraic structure of V.P. Potapov's Fundamental Matrix Inequality (FMI) is discussed and its interpolation meaning is analyzed. Functional model spaces are involved. A general Abstract Interpolation Problem is formulated which seems to cover all the classical and recent problems in the field and the solution set of this problem is described using the Arov--Grossman formula. The extension theory of isometric operators is the proper language for treating interpolation problems of this type.

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