The commutant lifting approach to interpolation problems [electronic resource] / Ciprian Foias, Arthur E. Frazho.
Classical H̃ 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 interpo...
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| Online Access: |
Full Text (via Springer) |
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| Main Author: | |
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel ; Boston :
Birkhäuser,
1990.
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| Series: | Operator theory, advances and applications ;
v. 44. |
| Subjects: |
| Summary: | Classical H̃ 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 H̃. At about the sametime as Sarason's work, V.M. |
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| Physical Description: | 1 online resource (xxiii, 632 pages) |
| Bibliography: | Includes bibliographical references ([599]-623) and index. |
| ISBN: | 9783034877121 3034877129 9783034877145 3034877145 |
| Language: | English. |
| Source of Description, Etc. Note: | Print version record. |