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This book is composed of three survey lecture courses and nineteen invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, which was held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction with research fields in complex analysis and operator theory. The lecture courses are: Subalgebras of Graph C*-algebras, by Stephen Power: An introduction to two classes of non-selfadjoint operator algebras, the generalized analytic Toeplitz algebras associated with the Fock space of a graph and subalgebras of graph C*-algebras; C*-algebras and asymptotic spectral theory, by Bernd Silbermann: Three topics on numerical functional analysis that are the cornerstones in asymptotic spectral theory: stability, fractality and Fredholmness; Toeplitz operator algebras and complex analysis, by Harald Upmeier: A survey concerning Hilbert spaces of holomorphic functions on Hermitian symmetric domains of arbitrary rank and dimension, in relation to operator theory, harmonic analysis and quantization.

Operator theory --- Algebra. --- Functional analysis. --- Operator theory. --- Functional Analysis. --- Operator Theory. --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematics --- Mathematical analysis --- Operator algebras --- WOAT

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This book is devoted to the spectral theory of commutative C*-algebras of Toeplitz operators on the Bergman space and its applications. For each such commutative algebra there is a unitary operator which reduces Toeplitz operators from this algebra to certain multiplication operators, thus providing their spectral type representations. This yields a powerful research tool giving direct access to the majority of the important properties of the Toeplitz operators studied herein, such as boundedness, compactness, spectral properties, invariant subspaces. The presence and exploitation of these spectral type representations forms the core for many results presented in the book. Among other results it contains a criterion of when the algebras are commutative on each commonly considered weighted Bergman space together with their explicit descriptions; a systematic study of Toeplitz operators with unbounded symbols; a clarification of the difference between compactness of commutators and semi-commutators of Toeplitz operators; the theory of Toeplitz and related operators with symbols having more than two limit values at boundary points; and a kind of semi-classical analysis of spectral properties of Toeplitz operators. The book is addressed to a wide audience of mathematicians, from graduate students to researchers, whose primary interests lie in complex analysis and operator theory. .

Bergman spaces. --- Commutative algebra. --- Toeplitz operators. --- Operator theory. --- Functions of complex variables. --- Functional analysis. --- Operator Theory. --- Functions of a Complex Variable. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Complex variables --- Elliptic functions --- Functions of real variables --- Functional analysis --- Functions of several complex variables --- Operators, Toeplitz --- Linear operators --- Algebra

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Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006. Requires no preliminary knowledge of graduate and advanced mathematics Discusses the fundamental results of last 15 years in this theo

Quantum theory. --- Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics

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Set-valued analysis is an essential tool for the mathematical formulation of many real-life situations, e.g., equilibrium theory in mathematical economics. This work offers the first comprehensive treatment in book form of the fairly new subdiscipline of enlargements of maximal monotone operators, including several important new results in the field. In the last decades, with the development of nonsmooth optimization, effective algorithms have been developed to solve these kinds of problems, such as nonsmooth variational inequalities. Several of these methods, such as bundle methods for variational problems, are fully developed and analyzed in this book. The first chapters provide a self-contained review of the basic notions and fundamental results in set-valued analysis, including set convergence and continuity of set-valued mappings together with many important results in infinite-dimensional convex analysis, leading to the classical fixed point results due to Ekeland, Caristi and Kakutani. Next, an in-depth introduction to monotone operators is developed, emphasizing results related to maximality of subdifferentials and of sums of monotone operators. Building on this foundational material, the second part of the monograph contains new results (all of them established during the last decade) on the concept of enlargements of monotone operators, with applications to variational inequalities, bundle-type methods, augmented Lagrangian methods, and proximal point algorithms. Audience This book is addressed to mathematicians, engineers, economists, and researchers interested in acquiring a solid mathematical foundation in topics such as point-to-set operators, variational inequalities, general equilibrium theory, and nonsmooth optimization, among others. Containing extensive exercises and examples throughout the text, the first four chapters of the book can also be used for a one-quarter course in set-valued analysis and maximal monotone operators for graduate students in pure and applied mathematics, mathematical economics, operations research and related areas. The only requisites, besides a minimum level of mathematical maturity, are some basic results of general topology and functional analysis.

Monotone operators. --- Operator theory. --- Functional analysis --- Operator theory --- Functional analysis. --- Mathematical optimization. --- Operations research. --- Functional Analysis. --- Optimization. --- Operator Theory. --- Operations Research, Management Science. --- Operations Research/Decision Theory. --- Calculus of Variations and Optimal Control; Optimization. --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Management science. --- Decision making. --- Calculus of variations. --- Isoperimetrical problems --- Variations, Calculus of --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Quantitative business analysis --- Statistical decision --- Decision making

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The use of various types of wave energy is an increasingly promising, non-destructive means of detecting objects and of diagnosing the properties of quite complicated materials. An analysis of this technique requires an understanding of how waves evolve in the medium of interest and how they are scattered by inhomogeneities in the medium. These scattering phenomena can be thought of as arising from some perturbation of a given, known system and they are analysed by developing a scattering theory. This monograph provides an introductory account of scattering phenomena and a guide to the technical requirements for investigating wave scattering problems. It gathers together the principal mathematical topics which are required when dealing with wave propagation and scattering problems, and indicates how to use the material to develop the required solutions. Both potential and target scattering phenomena are investigated and extensions of the theory to the electromagnetic and elastic fields are provided. Throughout, the emphasis is on concepts and results rather than on the fine detail of proof; a bibliography at the end of each chapter points the interested reader to more detailed proofs of the theorems and suggests directions for further reading. Aimed at graduate and postgraduate students and researchers in mathematics and the applied sciences, this book aims to provide the newcomer to the field with a unified, and reasonably self-contained, introduction to an exciting research area and, for the more experienced reader, a source of information and techniques.

Mathematics. --- Functional Analysis. --- Operator Theory. --- Partial Differential Equations. --- Functional analysis. --- Operator theory. --- Differential equations, partial. --- Mathématiques --- Analyse fonctionnelle --- Théorie des opérateurs --- Scattering (Mathematics). --- Scattering (Physics) -- Mathematics. --- Waves -- Mathematics. --- Scattering (Physics) --- Scattering (Mathematics) --- Waves --- Scattering theory (Mathematics) --- Atomic scattering --- Atoms --- Nuclear scattering --- Particles (Nuclear physics) --- Scattering of particles --- Wave scattering --- Scattering --- Physics. --- Partial differential equations. --- Optics. --- Electrodynamics. --- Optics and Electrodynamics. --- Dynamics --- Physics --- Light --- Partial differential equations --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Cycles --- Hydrodynamics --- Benjamin-Feir instability --- Boundary value problems --- Differential equations, Partial --- Scattering operator --- Collisions (Nuclear physics) --- Particles --- Collisions (Physics) --- Classical Electrodynamics.