Concise treatment focuses on theory of shift operators, Toeplitz operators and Hardy classes of vector- and operator-valued functions. Topics include general theory of shift operators on a Hilbert space, use of lifting theorem to give a unified treatment of interpolation theorems of the Pick-Nevanlinna and Loewner types, more. Appendix. Bibliography. 1985 edition.

Hardy Classes and Operator Theory (Oxford Mathematical Monographs)

Science & Math

Rosenblum, Marvin

Rovnyak, James

Mathematics

Oxford University Press

Concise treatment focuses on theory of shift operators, Toeplitz operators and Hardy classes of vector- and operator-valued functions. Topics include general theory of shift operators on a Hilbert space, use of lifting theorem to give a unified treatment of interpolation theorems of the Pick-Nevanlinna and Loewner types, more. Appendix. Bibliography. 1985 edition.

Hardy Classes

Dover Publications

This text for advanced undergraduate and graduate students introduces Hilbert space and analytic function theory, which is centered around the invariant subspace concept. The book's principal feature is the extensive use of formal power series methods to obtain and sometimes reformulate results of analytic function theory. The presentation is elementary in that it requires little previous knowledge of analysis, but it is designed to lead students to an advanced level of performance. This is achieved chiefly through the use of problems, many of which were proposed by former students. The book's tried-and-true approach was developed from the authors' lecture notes on courses taught at Lafayette College, Bryn Mawr College, and Purdue University.

Square Summable Power Series (Dover Books on Mathematics)

De Branges, Louis

Much of the importance of mathematics lies in its ability to provide theories which are useful in widely different fields of endeavor. A good example is the large and amorphous body of knowledge known as ``the theory of linear operators'' or ``operator theory'', which came to life about a century ago as a theory to encompass properties common to matrix, differential, and integral operators. Thus, it is a primary purpose of operator theory to provide a coherent body of knowledge which can explain phenomena common to the enormous variety of problems in which such linear operators play a part. The theory is a vital part of ``functional analysis'', whose methods and techniques are one of the major advances of twentieth century mathematics and now play a pervasive role in the modeling of phenomena in probability, imaging, signal processing, systems theory, etc., as well as in the more traditional areas of theoretical physics and mechanics. This book is based on lectures presented at a meeting on operator theory and its applications held at the Fields Institute in the fall of 1994. The purpose of the meeting was to provide introductory lectures on some of the methods being used and problems being tackled in current research involving operator theory.

Lectures on Operator Theory and Its Applications (Fields Institute Monographs, 3)

Kaashoek, M. A.

Dijksma, Aad

Langer, Heinz

Dritschel, Michael A.

Amer Mathematical Society

These notes are based on lectures given at the University of Virginia over the past twenty years. They may be viewed as a course in function theory for nonspecialists. Chapters 1-6 give the function-theoretic background to Hardy Classes and Operator Theory, Oxford Mathematical Monographs, Oxford University Press, New York, 1985. These chapters were written first, and they were origi nally intended to be a part of that book. Half-plane function theory continues to be useful for applications and is a focal point in our account (Chapters 5 and 6). The theory of Hardy and Nevanlinna classes is derived from proper ties of harmonic majorants of subharmonic functions (Chapters 3 and 4). A selfcontained treatment of harmonic and subharmonic functions is included (Chapters 1 and 2). Chapters 7-9 present concepts from the theory of univalent functions and Loewner families leading to proofs of the Bieberbach, Robertson, and Milin conjectures. Their purpose is to make the work of de Branges accessible to students of operator theory. These chapters are by the second author. There is a high degree of independence in the chapters, allowing the material to be used in a variety of ways. For example, Chapters 5-6 can be studied alone by readers familiar with function theory on the unit disk. Chapters 7-9 have been used as the basis for a one-semester topics course.

Topics in Hardy Classes and Univalent Functions (Birkhäuser Advanced Texts Basler Lehrbücher)

Birkhauser

Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproducing kernel Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, Krein-Langer factorizations, and other topics. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is self-contained and streamlined so that the indefinite case is handled completely parallel to the definite case.

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces (Operator Theory: Advances and Applications)

Alpay, Daniel

Snoo, Hendrik de

Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproducing kernel Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, Krein-Langer factorizations, and other topics. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is self-contained and streamlined so that the indefinite case is handled completely parallel to the definite case.

Birkhäuser Basel

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Books by Rovnyak, James

See the best price to sell, buy, or rent books by Rovnyak, James. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Hardy Classes and Operator Theory (Oxford Mathematical Monographs)

Hardy Classes

Square Summable Power Series (Dover Books on Mathematics)

Lectures on Operator Theory and Its Applications (Fields Institute Monographs, 3)

Topics in Hardy Classes and Univalent Functions (Birkhäuser Advanced Texts Basler Lehrbücher)

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces (Operator Theory: Advances and Applications)

Topics in Hardy Classes and Univalent Functions (Birkhäuser Advanced Texts Basler Lehrbücher)

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces (Operator Theory: Advances and Applications)