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Metric Constrained Interpolation, Commutant Lifting and Systems
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Metric Constrained Interpolation, Commutant Lifting and Systems

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Metric Constrained Interpolation, Commutant Lifting and Systems

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Beschreibung

Details

Einband

Taschenbuch

Erscheinungsdatum

17.10.2012

Verlag

Springer Basel

Seitenzahl

587

Maße (L/B/H)

23.5/15.5/3.3 cm

Gewicht

914 g

Auflage

Softcover reprint of the original 1st ed. 1998

Sprache

Englisch

ISBN

978-3-0348-9775-4

Beschreibung

Details

Einband

Taschenbuch

Erscheinungsdatum

17.10.2012

Verlag

Springer Basel

Seitenzahl

587

Maße (L/B/H)

23.5/15.5/3.3 cm

Gewicht

914 g

Auflage

Softcover reprint of the original 1st ed. 1998

Sprache

Englisch

ISBN

978-3-0348-9775-4

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  • Metric Constrained Interpolation, Commutant Lifting and Systems
  • A Interpolation And Time-Invariant Systems.- I. Interpolation Problems For Operator-Valued Functions.- 1.1. Preliminaries About Notation And Terminology.- 1.2. Nevanlinna-Pick Interpolation.- 1.3. Tangential Nevanlinna-Pick Interpolation.- 1.4. Controllability Operators And Interpolation.- 1.5. Tangential Hermite-Fejer Interpolation.- 1.6. The Nehari Extension Problem.- 1.7. Sarason Interpolation.- 1.8. Nevanlinna-Pick Interpolation Viewed As A Sarason Problem.- 1.9. Two-Sided Nudelman Interpolation.- 1.10. The Two-Sided Sarason Problem.- 1.11. A Filtering Problem.- Notes To Chapter I.- II. Proofs Using The Commutant Lifting Theorem.- II.1. The Commutant Lifting Theorem.- II.2. Proof Of The Standard Left Nevanlinna-Pick Interpolation Theorem.- II.3. Proof Of The Nehari Extension Theorem.- II.4. Proof of the Sarason Theorem.- II.5. Proof of the Two-Sided Nudelman Theorem.- II.6. Proof of the Two-Sided Sarason Theorem.- Notes to Chapter II.- III. Time Invariant Systems.- III.1. State Space Analysis.- III.2. Controllability and Observability.- III.3. Point Evaluation.- III.4. Realization Theory.- III.5. Anticausal Realizations.- III.6. Computing the Hankel form.- III.7. Computing the Projection in the Sarason Problem.- III.8. Explicit Conversion Formulas.- III.9. Connecting Nudelman and Two-Sided Sarason Problems.- III.10. Isometric and Unitary Systems.- Notes to Chapter III.- IV. Central Commutant Lifting.- IV. 1. Minimal Isometric Liftings.- IV.2. The Central Intertwining Lifting.- IV.3. Central Intertwining Lifting Formulas.- IV.4. Central Intertwining Lifting Quotient Formulas.- IV.5. The Central Schur Solution.- IV.6. The Quasi Outer Factor for D2/By.- IV.7. Maximum Entropy.- IV.8. Some Mixed Bounds for the Central Intertwining Lifting.- IV.9. A Mixed Two-Sided Sarason Result.- Notes To Chapter IV.- V. Central State Space Solutions.- V.1. The Central Formula For Nevanlinna-Pick.- V.2. Central Nevanlinna-Pick Solutions.- V.3. The Central Hermite-Fejer Solution.- V.4. The Central Formula For The Sarason Problem.- V.5. Central Nehari Solutions.- V.6. Central Nudelman Solutions.- V.7. The Central Two Block Solution.- V.8. The Four Block Problem.- Notes To Chapter V.- VI. Parameterization Of Intertwining Liftings And Its Applications.- VI.1. The Möbius Transformation.- VI.2. The Schur Parameterization.- VI.3. Recovering The Schur Contraction..- VI. 4. Constructing The Schur Contraction.- VI.5. The Redheffer Scattering Parameterization.- VI.6. The Parameterization for A ?.- VI.7. The Nevalinna-Pick Parameterization.- VI.8. The Nehari Parameterization.- VI.9. The Two Block Parameterization.- Notes To Chapter VI.- VII. Applications to Control Systems.- VII. 1. Feedback Control.- VII.2. The Youla Parameterization.- VII.3. Mixed H? and H2 Control Problems.- VII.4. A Two Block Control Problem.- VII.5. The Multivariable Case.- Notes To Chapter VII.- B Nonstationary Interpolation and Time-Varying Systems.- VIII. Nonstationary Interpolation Theorems.- VIII.1. Nonstationary Nevanlinna-Pick Interpolation.- VIII.2. Nonstationary Tangential Nevanlinna-Pick Interpolation.- VIII.3. Nonstationary Tangential Hermite-Fejer Interpolation.- VIII.4. Nonstationary Nehari Interpolation.- VIII.5. Nonstationary Sarason Interpolation.- VIII.6. Nonstationary Nudelman Interpolation.- VIII.7. Nonstationary Two-Sided Sarason Interpolation.- Notes to Chapter VIII.- IX. Nonstationary Systems and Point Evaluation.- IX.1. Time Varying Systems.- IX.2. Nonstationary Controllability and Observability.- IX.3. Point Evaluation.- IX.4. From Nonstationary Systems to Stationary Systems.- IX.5. A Nonstationary Filtering Problem.- Notes to Chapter IX.- X. Reduction Techniques: From Nonstationary to Stationary and Vice Versa.- X.1. Spatial Features.- X.2. Operator Features.- Notes to Chapter X.- XI. Proofs of the Nonstationary Interpolation Theorems by Reduction to the Stationary Case.- XI.1. The Standard Nonstationary Nevanlinna-Pick Interpolation Theorem.- XI.2. The Nonstationary Version of Neharf’S Theorem.- XI.3. The Nonstationary Sarason Interpolation Theorem.- XI.4. The Nonstationary Version of Nudelman’S Theorem.- XI.5. The Nonstationary Two-Sided Sarason Interpolation Theorem.- Notes To Chapter XI.- XII. A General Completion Theorem.- XII. 1. The Three Chains Completion Theorem.- XII.2. Proof by One Step Extensions.- XII.3. An Explicit Solution of the Three Chains Completion Problem.- XII.4. Maximum Entropy.- XII.5. A Quotient Formula for the Central Interpolant.- XII.6. The Caswell-Schubert Theorem.- Notes to Chapter XII..- XIII. Applications of the Three Chains Completion Theorem to Interpolation.- XIII.1. Abstract Nonstationary Interpolation.- XIII.2. Application to Nevanlinna-Pick Interpolation.- XIII.3. Application to the Nehari Problem.- XIII.4. Application to the Two-Sided Sarason Problem.- XIII.5. Application to the Nudelman Problem.- XIII.6. The Three Chains Completion Problem and the Four Block Problem.- Notes To Chapter XIII.- XIV. Parameterization of All Solutions of the Three Chains Completion Problem.- XIV.1. Main Theorem.- XIV.2. Proof Of Main Theorem (First Part).- XIV.3. Proof of Main Theorem (Second Part).- XIV.4. The Case of Decreasing Spaces.- XIV.5. The Nonstationary Nehari Parameterization.- Notes to Chapter XIV.- Appendix on Factorization of Matrix-Valued Functions.- A.1. Square Outer Spectral Factorizations.- A.2. Inner-Outer Factorizations.- Notes to Appendix.- References.- List of Symbols.