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The Commutant Lifting Approach to Interpolation Problems

✍ Scribed by Prof. Ciprian Foias, Prof. Arthur E. Frazho (auth.)

Publisher
BirkhΓ€user Basel
Year
1990
Tongue
English
Leaves
647
Series
OT 44 Operator Theory: Advances and Applications 44
Edition
1
Category
Library
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✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xxiii
Analysis of the Caratheodory Interpolation Problem....Pages 1-32
Analysis of the Caratheodory Interpolation Problem for Positive-Real Functions....Pages 33-52
Schur Numbers, Geophysics and Inverse Scattering Problems....Pages 53-70
Contractive Expansions on Euclidian and Hilbert Space....Pages 71-97
Contractive One Step Intertwining Liftings....Pages 99-121
Isometric and Unitary Dilations....Pages 123-151
The Commutant Lifting Theorem....Pages 153-190
Geometric Applications of the Commutant Lifting Theorem....Pages 191-232
H ∞ Optimization and Functional Models....Pages 233-274
Some Classical Interpolation Problems....Pages 275-326
Interpolation as a Momentum Problem....Pages 327-342
Numerical Algorithms for H ∞ Optimization in Control Theory....Pages 343-365
Inverse Scattering Algorithms for the Commutant Lifting Theorem....Pages 367-426
The Schur Representation....Pages 427-495
A Geometric Approach to Positive Definite Sequences....Pages 497-546
Positive Definite Block Matrices....Pages 547-586
A Physical Basis for the Layered Medium Model....Pages 587-598
Back Matter....Pages 599-632

✦ Subjects

Science, general

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