This monograph combines the commutant lifting theorem for operator theory and the state space method from system theory to provide a unified approach for solving both stationary and nonstationary interpolation problems with norm constraints. Included are the operator-valued versions of the tangential Nevanlinna-Pick problem, the Hermite-FejA(c)r problem, the Nehari problem, the Sarason problem, and the two-sided Nudelman problem, and their nonstationary analogues. The main results concern the existence of solutions, the explicit construction of the central solutions in state space form, the maximum entropy property of the central solutions, and state space parametrizations of all solutions. Direct connections between the various interpolation problems are displayed. Applications to H infinity] control problems are presented. This monograph should appeal to a wide group of mathematicians and engineers. The material is self-contained and may be used for advanced graduate courses and seminars.

This volume, dedicated to Carl Pearcy on the occasion of his 60th birthday, presents recent results in operator theory, nonselfadjoint operator algebras, measure theory and the theory of moments. The articles on these subjects have been contributed by leading area experts, many of whom were associated with Carl Pearcy as students or collaborators. The book testifies to his multifaceted interests and includes a biographical sketch and a list of publications.

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.

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.

Since its inception in the early 1980s, H( optimization theory has become the control methodology of choice in robust feedback analysis and design. The purpose of this monograph is to present, in a tutorial fashion, a self contained operator theoretic approach to the H( control for disturbed parameter systems, that is, systems which admit infinite dimensional state spaces. Such systems arise for problems modelled by partial differential equations or which have time delays. Besides elucidating the mathematics of H( control, extensive treatment is given to its physical and engineering underpinnings. The techniques given in the book are carefully illustrated by two benchmark problems: an unstable system with a time delay which comes from the control of the X-29, and the control of a Euler-Bernoulli flexible beam with Kelvin-Voigt damping.

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.

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.