The present book deals with canonical factorization problems for di?erent classes of matrix and operator functions. Such problems appear in various areas of ma- ematics and its applications. The functions we consider havein common that they appear in the state space form or can be represented in such a form. The main results are all expressed in terms of the matrices or operators appearing in the state space representation. This includes necessary and su?cient conditions for canonical factorizations to exist and explicit formulas for the corresponding f- tors. Also, in the applications the...
The present book deals with canonical factorization problems for di?erent classes of matrix and operator functions. Such problems appear in various ar...
The volume contains the proceedings of the OTAMP 2006 (Operator Theory, Analysis and Mathematical Physics) conference held at Lund University in June 2006. The conference was devoted to the methods of analysis and operator theory in modern mathematical physics. The following special sessions were organized: Spectral analysis of Schrodinger operators; Jacobi and CMV matrices and orthogonal polynomials; Quasi-periodic and random Schrodinger operators; Quantum graphs.
The volume contains the proceedings of the OTAMP 2006 (Operator Theory, Analysis and Mathematical Physics) conference held at Lund University in Ju...
Thepresentbookdealswithvarioustypesoffactorizationproblemsformatrixand operator functions. The problems appear in di?erent areasof mathematics and its applications. A uni?ed approach to treat them is developed. The main theorems yield explicit necessaryand su?cient conditions for the factorizations to exist and explicit formulas for the corresponding factors. Stability of the factors relative to a small perturbation of the original function is also studied in this book. The unifying theory developed in the book is based on a geometric approach which has its origins in di?erent ?elds. A number...
Thepresentbookdealswithvarioustypesoffactorizationproblemsformatrixand operator functions. The problems appear in di?erent areasof mathematics and its...
This book analyzes the existence and uniqueness of a generalized algebraic m- tiplicity for a general one-parameter family L of bounded linear operators with Fredholm index zero at a value of the parameter ? whereL(? ) is non-invertible. 0 0 Precisely, given K?{R, C}, two Banach spaces U and V over K, an open subset ? ? K, andapoint ? ? ?, our admissible operator families are the maps 0 r L?C (?, L(U, V)) (1) for some r? N, such that L(? )? Fred (U, V); 0 0 hereL(U, V) stands for the space of linear continuous operatorsfrom U to V, and Fred (U, V) is its subset consisting of all Fredholm...
This book analyzes the existence and uniqueness of a generalized algebraic m- tiplicity for a general one-parameter family L of bounded linear operato...
Operator theory and functional analysis have a long tradition, initially being guided by problems from mathematical physics and applied mathematics. Much of the work in Banach spaces from the 1930s onwards resulted from investigating how much real (and complex) variable function theory might be extended to fu- tions taking values in (function) spaces or operators acting in them. Many of the ?rst ideas in geometry, basis theory and the isomorphic theory of Banach spaces have vector measure-theoretic origins and can be credited (amongst others) to N. Dunford, I.M. Gelfand, B.J. Pettis and R.S....
Operator theory and functional analysis have a long tradition, initially being guided by problems from mathematical physics and applied mathematics. M...
This unique book is devoted to the detailed study of the recently discovered commutative C*-algebras of Toeplitz operators on the Bergman space over the unit disk. Surprisingly, the key point to understanding their structure and classifying them lies in the hyperbolic geometry of the unit disk. The book develops a number of important problems whose successful solution was made possible and is based on the specific features of the Toeplitz operators from these commutative algebras.
This unique book is devoted to the detailed study of the recently discovered commutative C*-algebras of Toeplitz operators on the Bergman space ove...
This book is designed to present some recent results on some nonlinear parabolic-hyp- bolic coupled systems arising from physics, mechanics and material science such as the compressible Navier-Stokes equations, thermo(visco)elastic systems and elastic systems. Some of the content of this book is based on research carried out by the author and his collaborators in recent years. Most of it has been previously published only in original papers, andsomeofthematerialhasneverbeenpublisheduntilnow.Therefore, theauthor hopes that the book will bene't both the interested beginner in the ?eld and the...
This book is designed to present some recent results on some nonlinear parabolic-hyp- bolic coupled systems arising from physics, mechanics and materi...
This volume contains the proceedings of the International Workshop on Operator Theory and Applications (IWOTA 2006) held at Seoul National University, Seoul, Korea, from July 31 to August 3, 2006. The special interest areas of this workshop were Hilbert/Krein space operator theory, complex function theory related to Hilbert space operators, and systems theory related to Hilbert space operators. This volume contains sixteen research papers which reflect recent developments in operator theory and applications.
This volume contains the proceedings of the International Workshop on Operator Theory and Applications (IWOTA 2006) held at Seoul National Universi...
Series of scalars, vectors, or functions are among the fundamental objects of mathematical analysis. When the arrangement of the terms is fixed, investigating a series amounts to investigating the sequence of its partial sums. In this case the theory of series is a part of the theory of sequences, which deals with their convergence, asymptotic behavior, etc. The specific character of the theory of series manifests itself when one considers rearrangements (permutations) of the terms of a series, which brings combinatorial considerations into the problems studied. The phenomenon that a...
Series of scalars, vectors, or functions are among the fundamental objects of mathematical analysis. When the arrangement of the terms is fixed, inves...
This book contains a collection of recent research papers originating from the 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, which was held at the TU Berlin, Germany, December 14 to 17, 2006. The contributions in this volume are devoted to spectral and perturbation theory of linear operators in spaces with an inner product, generalized Nevanlinna functions and problems and applications in the field of differential equations. Among the discussed topics are linear relations, singular perturbations, de Branges spaces, nonnegative matrices and abstract kinetic...
This book contains a collection of recent research papers originating from the 6th Workshop on Operator Theory in Krein Spaces and Operator Polynom...
