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The Commutant Lifting Approach to Interpolation Problems by Foias
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The Commutant Lifting Approach to Interpolation Problems

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Description

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.
Release date NZ
April 29th, 2013
Author
Audience
  • Professional & Vocational
Edition
Softcover reprint of the original 1st ed. 1990
Illustrations
XXIII, 632 p.
Pages
632
Dimensions
152x229x33
ISBN-13
9783034877145
Product ID
21698579

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