The Commutant Lifting Approach to Interpolation Problems

Foias

ISBN 10: 3034877145 / ISBN 13: 9783034877145

Published by Springer, Basel, Birkhäuser Basel, Birkhäuser Okt 2013, 2013

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 632 pp. Englisch.

Seller Inventory # 9783034877145

Bibliographic Details

• Title: The Commutant Lifting Approach to Interpolation Problems
• Publisher: Springer, Basel, Birkhäuser Basel, Birkhäuser Okt 2013
• Publication Date: 2013
• Language: English
• ISBN 10: 3034877145
• ISBN 13: 9783034877145
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 228W x 152H x 37D millimeters 228 millimeters width by 152 millimeters height by 37 millimeters depth
• Weight: 916 grams

About this title

Synopsis

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 Mobius 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.