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This unique book addresses advanced linear algebra from a perspective in which invariant subspaces are the central notion and main tool. It contains comprehensive coverage of geometrical, algebraic, topological, and analytic properties of invariant subspaces. The text lays clear mathematical foundations for linear systems theory and contains a thorough treatment of analytic perturbation theory for matrix functions.

Audience
This book is appropriate for students, instructors, and researchers in applied linear algebra, linear systems theory, and signal processing. Its contents are accessible to readers who have had undergraduate-level courses in linear algebra and complex function theory. ... Read more

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This book contains a selection of carefully refereed research papers, most of which were presented at the 14th International Workshop on Operator Theory and its Applications (IWOTA) held at Cagliari, Italy (June 24-27, 2003). The papers, many of which have been written by leading experts in the field, concern a wide variety of topics in modern operator theory and applications, with emphasis on differential operators and numerical methods. Included are papers on the structure of operators, spectral theory of differential operators, theory of pseudo-differential operators and Fourier integral operators, numerical methods for solving nonlinear integral equations, singular integral equations, and Toeplitz systems. Other main topics covered are inverse problems for canonical systems, factorization methods, metric constrained interpolation, mathematical system theory, and elements of multivariable operator theory. The book will be of interest to a wide audience of pure and applied mathematicians and engineers. ... Read more

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This book is dedicated to Israel Gohberg on occasion of his 80th birthday on August 23, 2008. It is an expression of esteem and friendship for a great mathematician, a remarkable person and an inspiring colleague. The book contains reflections by Gohberg himself on his own mathematical activities and those of others. It also includes contributions of colleagues and co-workers, both from his time in the Soviet Union and from when he lived and worked in the West. The contributions in question are not mathematical research papers but focus on the man Israel Gohberg and are intended for a wide audience. To be found are letters, speeches, laudatios and reminiscences which, together, present an attractive picture of the way in which Israel Gohberg in the past four to five decades influenced the lives of many mathematicians. Biographical material such as a curriculum vitae, a list of publications, a list of Ph.D. students and information about honorary doctoral degrees is also included.

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Contains papers in spectral theory of differential operators and linear operators in Hilbert and Banach spaces, analytic operator functions, ordinary and partial differential equations, functional equations, mathematical physics, and mathematical statistics. ... Read more

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The present book deals with canonical factorization of matrix and operator functions that appear in state space form or that can be transformed into such a form. A unified geometric approach is used. The main results are all expressed explicitly in terms of matrices or operators, which are parameters of the state space representation. The applications concern different classes of convolution equations: the transport equation, singular integral equations, Wiener-Hopf equations with symbols analytic in a strip, and equations involving factorization of non-proper rational matrix functions. The analysis of canonical factorization for functions with symmetries, including spectral and J-spectral factorizations, related Ricatti equations, and elements of H-infinity control theory are also main topics.

This book is the second book written by the four authors in which the state space factorization method is systematically used and developed further. In their first book, released in 2007, the emphasis is on non-canonical factorizations and degree one factorizations, in particular. The present book concentrates on canonical factorization and its applications. Together both books present a rich and far reaching update of the 1979 monograph, the first book in the OTAA series, written by the first three authors.

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Basic Operator Theory provides an introduction to functional analysis with an emphasis on the theory of linear operators and its application to differential and integral equations, approximation theory, and numerical analysis. A textbook designed for senior undergraduate and graduate students, Basic Operator Theory begins with the geometry of Hilbert space and proceeds to the spectral theory for compact self-adjoint operators with a wide range of applications. Part of the volume is devoted to Banach spaces and operators acting on these spaces.Presented as a natural continuation of linear algebra, Basic Operator Theory provides a firm foundation in operator theory, an essential part of mathematical training for students of mathematics, engineering, and other technical sciences. ... Read more

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This book covers recent results in linear algebra with indefinite inner product. It includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications are based on linear algebra in spaces with indefinite inner product. The latter forms an independent branch of linear algebra called indefinite linear algebra. This new subject is presented following the principles of a standard linear algebra course.

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This volume is devoted to the memory of the applied mathematician Erhard Meister (1930-2001). It is divided into two parts. Part A contains reminiscences about the life of E. Meister including a short biography and an exposition of his professional work. Part B displays the wide range of his scientific interests through eighteen original papers contributed by authors with close scientific and personal relations to Erhard Meister. It covers various fields of mathematical physics and its theoretical background such as partial differential equations, singular integral and pseudodifferential equations as well as topics from operator theory and complex analysis. Altogether fifty colleagues, friends and family members contributed to honour E. Meister as a researcher and promoter of science and succeeded in drawing a real picture of his life and work.

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The present book deals with factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, theory of job scheduling in operations research. The book systematically employs a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions. This principle allows one to deal with different factorizations from one point of view. Covered are canonical factorization, minimal and non-minimal factorizations, pseudo-canonical factorization, and various types of degree one factorization.

Considerable attention is given to the matter of stability of factorization which in terms of the state space method involves stability of invariant subspaces.invariant subspaces.

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Schur analysis originates with a 1917 paper by Schur where he associated to a function analytic and contractive in the open unit disk a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients. In signal processing, they are often called reflection coefficients. Under the word "Schur analysis" one encounters a variety of problems related to Schur functions such as interpolation problems, moment problems, study of the relationships between the Schur coefficients and the properties of the function, study of underlying operators and others.

This volume is almost entirely dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes.

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This book consists of a careful selection of peer-reviewed articles originating from the 19th International Conference on Operator Theory, held in Timisoara in Summer 2002. It contains recent developments covering a broad range of topics from operator theory, operator algebras and their applications, particularly to differential analysis, complex functions, ergodic theory, mathematical physics, matrix analysis, and systems theory.

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This volume, dedicated to Bernd Silbermann on his sixtieth birthday, collects research articles on Toeplitz matrices and singular integral equations written by leading area experts.

The subjects of the contributions include Banach algebraic methods, Toeplitz determinants and random matrix theory, Fredholm theory and numerical analysis for singular integral equations, and efficient algorithms for linear systems with structured matrices, and reflect Bernd Silbermann's broad spectrum of research interests. The volume also contains a biographical essay and a list of publications.

The book is addressed to a wide audience in the mathematical and engineering sciences. The articles are carefully written and are accessible to motivated readers with basic knowledge in functional analysis and operator theory. ... Read more

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In September 2000 a Summer School on 'Factorization and Integrable Systems' was held at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems. The program consisted of a number of short courses given by leading experts in the field. The lecture notes of the courses have been specially prepared for publication in this volume.
The book consists of four contributions. I. Gohberg, M.A. Kaashoek and I.M. Spitkovsky present an extensive review of the factorization theory of matrix functions relative to a curve, with emphasis on the developments of the last 20-25 years. The group-theoretical approach to classical integrable systems is reviewed by M.A. Semenov-Tian-Shansky. P.P. Kulish surveyed the quantum inverse scattering method using the isotropic Heisenberg spin chain as the main example.

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This volume presents the proceedings of the 11th Conference on Problems and Methods in Mathematical Physis (11th TMP), held in Chemnitz, March 25-28, 1999.

The conference was dedicated to the memory of Siegfried Prössdorf, who made important contributions to the theory and numerical analysis of operator equations and their applications in mathematical physics and mechanics.The main part of the book comprises original research papers. The topics are ranging from integral and pseudodifferential equations, boundary value problems, operator theory, boundary element and wavelet methods, approximation theory and inverse problems to various concrete problems and applications in physics and engineering, and reflect Prössdorf's broad spectrum of research activities. The volume also contains articles describing the life and mathematical achievements of Siegfried Prössdorf and includes a list of his publications.The book is addressed to a wide audience in the mathematical and engineering sciences. ... Read more

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The present book is the first of the two volume proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine, from August 18-22, 1997. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein.

This first volume is devoted to the theory of differential operators and related topics. It opens with a description of the conference, biographical material and a number of survey papers about the work of M. G. Krein. The main part of the book consists of original research papers presenting the state of the art in the area of differential operators. The second volume of these proceedings, entitled Operator Theory and Related Topics, concerns the other aspects of the conference. The two volumes will be of interest to a wide range of readership in pure and applied mathematics, physics and engineering sciences.

Series: Operator Theory: Advances and Applications, Vol. 117 ... Read more

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Contributed volume in honor of Peter Lancaster, an outstanding expert in operator theory, matrix theory and numerical analysis. The articles have been carefully selected and refereed and cover topics in linear algebra and analysis where Peter Lancaster was very active.The book is complemented by biographical information.

This volume is dedicated to Peter Lancaster, an outstanding expert in operator and matrix theory, numerical analysis and applications, on the occasion of his seventieth birthday.The book contains a selection of recent original research papers in linear algebra and analysis, areas in which Peter Lancaster was very active. The articles are complemented by biographical data and a list of publications. ... Read more