Commutant lifting approach to interpolation problems
Foias, Ciprian
Commutant lifting approach to interpolation problems - Switzerland : Springer Basel AG, 1990. - xxiii, 632p. : 24 cm. - Operator theory, advances and applications ; v. 44 .
Includes bibliographical references and index.
Classical H~ interpolation theory was conceived at the beginning of the century by C. Caratheodory, L. Fejer and I. Schur. The basic method, due to Schur, in solving these problems consists in applying the Möbius transform to peel off the data. In 1967, D. Sarason encompassed these classical interpolation problems in a representation theorem of operators commuting with special contractions. Shortly after that, in 1968, B. Sz. Nagy and C. Foias obtained a purely geometrical extension of Sarason's results. Actually, their result states that operators intertwining restrictions of co-isometries can be extended, by preserving their norm, to operators intertwining these co-isometries; starring with R.G. Douglas, P.S. Muhly and C. Pearcy, this is referred to as the commutant lifting theorem. In 1957, Z. Nehari considered an L ~ interpolation problern which in turn encompassed the same classical interpolation problems, as well as the computation of the distance of a function f in L ~ to H~. At about the sametime as Sarason's work, V.M.
9783034877145
Interpolation.
Lifting theory.
Boundary element method
Control theory
Hilbert space
Mathematical programming
Matrices
517.518.85 / FOI-C
Commutant lifting approach to interpolation problems - Switzerland : Springer Basel AG, 1990. - xxiii, 632p. : 24 cm. - Operator theory, advances and applications ; v. 44 .
Includes bibliographical references and index.
Classical H~ interpolation theory was conceived at the beginning of the century by C. Caratheodory, L. Fejer and I. Schur. The basic method, due to Schur, in solving these problems consists in applying the Möbius transform to peel off the data. In 1967, D. Sarason encompassed these classical interpolation problems in a representation theorem of operators commuting with special contractions. Shortly after that, in 1968, B. Sz. Nagy and C. Foias obtained a purely geometrical extension of Sarason's results. Actually, their result states that operators intertwining restrictions of co-isometries can be extended, by preserving their norm, to operators intertwining these co-isometries; starring with R.G. Douglas, P.S. Muhly and C. Pearcy, this is referred to as the commutant lifting theorem. In 1957, Z. Nehari considered an L ~ interpolation problern which in turn encompassed the same classical interpolation problems, as well as the computation of the distance of a function f in L ~ to H~. At about the sametime as Sarason's work, V.M.
9783034877145
Interpolation.
Lifting theory.
Boundary element method
Control theory
Hilbert space
Mathematical programming
Matrices
517.518.85 / FOI-C
