Commutant lifting approach to interpolation problems
Material type:
TextLanguage: English Series: Operator theory, advances and applications ; v. 44Publication details: Switzerland : Springer Basel AG, 1990. Description: xxiii, 632p. : 24 cmISBN: 9783034877145Subject(s): Interpolation | Lifting theory | Boundary element method | Control theory | Hilbert space | Mathematical programming | MatricesDDC classification: 517.518.85 Online resources: Table of contents | Reviews Summary: 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.
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
Book
|
SMS Library | 517.518.85 FOI-C (Browse shelf(Opens below)) | Available | 25150 |
Browsing SMS Library shelves Close shelf browser (Hides shelf browser)
| 517.518.24 AMB-F Functions of bounded variation and free discontinuity problems | 517.518.28 VEN-I Inequalities: An approach through problems | 517.518.45 HUY-F Fourier-Mukai transforms in algebraic geometry | 517.518.85 FOI-C Commutant lifting approach to interpolation problems | 517.53 BER-C Complex variables: an introduction | 517.53 BRO-C Complex variable and applications | 517.53 CAR-T Theory of functions of a complex variable volume: 1 |
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.
There are no comments on this title.