Ciprian Foias's Books

Harmonic Analysis of Operators on Hilbert Space

By: Béla Sz Nagy,Ciprian Foias,Hari Bercovici,László Kérchy

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Harmonic Analysis of Operators on Hilbert Space

By: Béla Sz Nagy,Ciprian Foias,Hari Bercovici,László Kérchy

The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.

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481

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Springer Science & Business Media

Published Date

ISBN 10

1441960937

ISBN 13

9781441960931

Navier-Stokes Equations

By: Peter Constantin,Ciprian Foias

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Navier-Stokes Equations

By: Peter Constantin,Ciprian Foias

Both an original contribution and a lucid introduction to mathematical aspects of fluid mechanics, Navier-Stokes Equations provides a compact and self-contained course on these classical, nonlinear, partial differential equations, which are used to describe and analyze fluid dynamics and the flow of gases.

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201

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University of Chicago Press

Published Date

ISBN 10

022676432X

ISBN 13

9780226764320

Metric Constrained Interpolation, Commutant Lifting, and Systems

By: Ciprian Foiaş

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Metric Constrained Interpolation, Commutant Lifting, and Systems

By: Ciprian Foiaş

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 Nons

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Page Count

610

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764358890

ISBN 13

9783764358891

Attractors Representing Turbulent Flows

By: Peter Constantin,Ciprian Foiaş,Roger Temam

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Attractors Representing Turbulent Flows

By: Peter Constantin,Ciprian Foiaş,Roger Temam

The purpose of this article is to fill some part of the gap existing between the mathematical theory of the Navier-Stokes equations and the conventional theory of turbulence and to provide a rigorous connection between these theories.

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American Mathematical Soc.

Published Date

ISBN 10

0821823159

ISBN 13

9780821823156

Attractors Representing Turbulent Flows

By: Peter Constantin,Ciprian Foiaş,Roger Temam

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Attractors Representing Turbulent Flows

By: Peter Constantin,Ciprian Foiaş,Roger Temam

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American Mathematical Soc.

Published Date

ISBN 10

0821823159

ISBN 13

9780821823156

Navier-Stokes Equations

By: Peter Constantin,Ciprian Foias

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Navier-Stokes Equations

By: Peter Constantin,Ciprian Foias

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Page Count

201

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University of Chicago Press

Published Date

ISBN 10

022676432X

ISBN 13

9780226764320

Harmonic Analysis of Operators on Hilbert Space

By: Béla Sz Nagy,Ciprian Foias,Hari Bercovici,László Kérchy

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Harmonic Analysis of Operators on Hilbert Space

By: Béla Sz Nagy,Ciprian Foias,Hari Bercovici,László Kérchy

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481

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Springer Science & Business Media

Published Date

ISBN 10

1441960937

ISBN 13

9781441960931

Turbulence in Fluid Flows

A Dynamical Systems Approach

By: George R. Sell,Ciprian Foias,Roger Temam

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Turbulence in Fluid Flows

A Dynamical Systems Approach

By: George R. Sell,Ciprian Foias,Roger Temam

The articles in this volume are based on recent research on the phenomenon of turbulence in fluid flows collected by the Institute for Mathematics and its Applications. This volume looks into the dynamical properties of the solutions of the Navier-Stokes equations, the equations of motion of incompressible, viscous fluid flows, in order to better understand this phenomenon. Although it is a basic issue of science, it has implications over a wide spectrum of modern technological applications. The articles offer a variety of approaches to the Navier-Stokes problems and related issues. This book should be of interest to both applied mathematicians and engineers.

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Page Count

220

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Springer Science & Business Media

Published Date

ISBN 10

0387941134

ISBN 13

9780387941134

Book's by Ciprian Foias

Harmonic Analysis of Operators on Hilbert Space

Harmonic Analysis of Operators on Hilbert Space

Navier-Stokes Equations

Navier-Stokes Equations

Metric Constrained Interpolation, Commutant Lifting, and Systems

Metric Constrained Interpolation, Commutant Lifting, and Systems

Attractors Representing Turbulent Flows

Attractors Representing Turbulent Flows

Attractors Representing Turbulent Flows

Attractors Representing Turbulent Flows

Navier-Stokes Equations

Navier-Stokes Equations

Harmonic Analysis of Operators on Hilbert Space

Harmonic Analysis of Operators on Hilbert Space

Turbulence in Fluid Flows

Turbulence in Fluid Flows

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