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The commutant lifting approach to interpolation problems [electronic resource] / Ciprian Foias, Arthur E. Frazho.

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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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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Foiaş, Ciprian
Other Authors: Frazho, Arthur E., 1950-
Format: Electronic eBook
Language:English
Published: Basel ; Boston : Birkhäuser, 1990.
Series:Operator theory, advances and applications ; v. 44.
Subjects:
Interpolation.
Lifting theory.
Table of Contents:
  • I. Analysis of the Caratheodory Interpolation Problem
  • II. Analysis of the Caratheodory Interpolation Problem for Positive-Real Functions
  • III. Schur Numbers, Geophysics and Inverse Scattering Problems
  • IV. Contractive Expansions on Euclidian and Hilbert Space
  • V. Contractive One Step Intertwining Liftings
  • VI. Isometric and Unitary Dilations
  • VII. The Commutant Lifting Theorem
  • VIII. Geometric Applications of the Commutant lifting Theorem
  • IX. H? Optimization and Functional Models
  • X. Some Classical Interpolation Problems
  • XI. Interpolation as a Momentum Problem
  • XII. Numerical Algorithms for H? Optimization in Control Theory
  • XIII. Inverse Scattering Algorithms for the Commutant Lifting Theorem
  • XIV. The Schur Representation
  • XV. A Geometric Approach to Positive Definite Sequences
  • XVI. Positive Definite Block Matrices
  • XVII. A Physical Basis for the Layered Medium Model
  • References
  • Notation.

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