Download or read book Introduction to the Theory of Linear Nonselfadjoint Operators written by Israel Gohberg and published by American Mathematical Soc.. This book was released on 1978 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discovering Modern Set Theory II Set Theoretic Tools for Every Mathematician written by Winfried Just and Martin Weese and published by American Mathematical Soc.. This book was released on with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theoretical Foundations of Functional Data Analysis with an Introduction to Linear Operators written by Tailen Hsing and published by John Wiley & Sons. This book was released on 2015-05-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.
Download or read book Discovering Modern Set Theory I The Basics written by Winfried Just and published by American Mathematical Soc.. This book was released on 1996 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book bridges the gap between the many elementary introductions to set theory that are available today and the more advanced, specialized monographs. The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.
Download or read book History of Banach Spaces and Linear Operators written by Albrecht Pietsch and published by Springer Science & Business Media. This book was released on 2007-12-31 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Download or read book An Introduction to Hankel Operators written by Jonathan R. Partington and published by Cambridge University Press. This book was released on 1988 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.
Download or read book Non Selfadjoint Operators in Quantum Physics written by Fabio Bagarello and published by John Wiley & Sons. This book was released on 2015-09-09 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features: Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.
Download or read book Introduction to Operator Space Theory written by Gilles Pisier and published by Cambridge University Press. This book was released on 2003-08-25 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory of operator spaces, emphasising applications to C*-algebras.
Download or read book Factorization Singular Operators and Related Problems written by Stefan Samko and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings comprise a large part of the papers presented at the In ternational Conference Factorization, Singular Operators and related problems, which was held from January 28 to February 1, 2002, at the University of th Madeira, Funchal, Portugal, to mark Professor Georgii Litvinchuk's 70 birth day. Experts in a variety of fields came to this conference to pay tribute to the great achievements of Professor Georgii Litvinchuk in the development of vari ous areas of operator theory. The main themes of the conference were focussed around the theory of singular type operators and factorization problems, but other topics such as potential theory and fractional calculus, to name but a couple, were also presented. The goal of the conference was to bring together mathematicians from var ious fields within operator theory and function theory in order to highlight recent advances in problems many of which were originally studied by Profes sor Litvinchuk and his scientific school. A second aim was to stimulate in ternational collaboration even further and promote the interaction of different approaches in current research in these areas. The Proceedings will be of great interest to researchers in Operator The ory, Real and Complex Analysis, Functional and Harmonic Analysis, Potential Theory, Fractional Calculus and other areas, as well as to graduate students looking for the latest results.
Download or read book Jacobi Matrices and the Moment Problem written by Yurij M. Berezansky and published by Springer Nature. This book was released on 2024-01-06 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the solution of the classical moment problem, the construction of Jacobi matrices and corresponding polynomials. The cases of strongly,trigonometric, complex and real two-dimensional moment problems are discussed, and the Jacobi-type matrices corresponding to the trigonometric moment problem are shown. The Berezansky theory of the expansion in generalized eigenvectors for corresponding set of commuting operators plays the key role in the proof of results. The book is recommended for researchers in fields of functional analysis, operator theory, mathematical physics, and engineers who deal with problems of coupled pendulums.
Download or read book Nonlinear Dirac Equation Spectral Stability of Solitary Waves written by Nabile Boussaïd and published by American Mathematical Soc.. This book was released on 2019-11-21 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves. The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrödinger equation. It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves the general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation.
Download or read book Ordinary Differential Equations and Integral Equations written by C.T.H. Baker and published by Elsevier. This book was released on 2001-06-20 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: /homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! This volume contains contributions in the area of differential equations and integral equations. Many numerical methods have arisen in response to the need to solve "real-life" problems in applied mathematics, in particular problems that do not have a closed-form solution. Contributions on both initial-value problems and boundary-value problems in ordinary differential equations appear in this volume. Numerical methods for initial-value problems in ordinary differential equations fall naturally into two classes: those which use one starting value at each step (one-step methods) and those which are based on several values of the solution (multistep methods).John Butcher has supplied an expert's perspective of the development of numerical methods for ordinary differential equations in the 20th century. Rob Corless and Lawrence Shampine talk about established technology, namely software for initial-value problems using Runge-Kutta and Rosenbrock methods, with interpolants to fill in the solution between mesh-points, but the 'slant' is new - based on the question, "How should such software integrate into the current generation of Problem Solving Environments?"Natalia Borovykh and Marc Spijker study the problem of establishing upper bounds for the norm of the nth power of square matrices.The dynamical system viewpoint has been of great benefit to ODE theory and numerical methods. Related is the study of chaotic behaviour.Willy Govaerts discusses the numerical methods for the computation and continuation of equilibria and bifurcation points of equilibria of dynamical systems.Arieh Iserles and Antonella Zanna survey the construction of Runge-Kutta methods which preserve algebraic invariant functions.Valeria Antohe and Ian Gladwell present numerical experiments on solving a Hamiltonian system of Hénon and Heiles with a symplectic and a nonsymplectic method with a variety of precisions and initial conditions.Stiff differential equations first became recognized as special during the 1950s. In 1963 two seminal publications laid to the foundations for later development: Dahlquist's paper on A-stable multistep methods and Butcher's first paper on implicit Runge-Kutta methods.Ernst Hairer and Gerhard Wanner deliver a survey which retraces the discovery of the order stars as well as the principal achievements obtained by that theory.Guido Vanden Berghe, Hans De Meyer, Marnix Van Daele and Tanja Van Hecke construct exponentially fitted Runge-Kutta methods with s stages.Differential-algebraic equations arise in control, in modelling of mechanical systems and in many other fields.Jeff Cash describes a fairly recent class of formulae for the numerical solution of initial-value problems for stiff and differential-algebraic systems.Shengtai Li and Linda Petzold describe methods and software for sensitivity analysis of solutions of DAE initial-value problems.Again in the area of differential-algebraic systems, Neil Biehn, John Betts, Stephen Campbell and William Huffman present current work on mesh adaptation for DAE two-point boundary-value problems.Contrasting approaches to the question of how good an approximation is as a solution of a given equation involve (i) attempting to estimate the actual error (i.e., the difference between the true and the approximate solutions) and (ii) attempting to estimate the defect - the amount by which the approximation fails to satisfy the given equation and any side-conditions.The paper by Wayne Enright on defect control relates to carefully analyzed techniques that have been proposed both for ordinary differential equations and for delay differential equations in which an attempt is made to control an estimate of the size of the defect.Many phenomena incorporate noise, and the numerical solution of
Download or read book Fundamentals of Functional Analysis written by Douglas Farenick and published by Springer. This book was released on 2016-10-24 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unique path for graduate or advanced undergraduate students to begin studying the rich subject of functional analysis with fewer prerequisites than is normally required. The text begins with a self-contained and highly efficient introduction to topology and measure theory, which focuses on the essential notions required for the study of functional analysis, and which are often buried within full-length overviews of the subjects. This is particularly useful for those in applied mathematics, engineering, or physics who need to have a firm grasp of functional analysis, but not necessarily some of the more abstruse aspects of topology and measure theory normally encountered. The reader is assumed to only have knowledge of basic real analysis, complex analysis, and algebra. The latter part of the text provides an outstanding treatment of Banach space theory and operator theory, covering topics not usually found together in other books on functional analysis. Written in a clear, concise manner, and equipped with a rich array of interesting and important exercises and examples, this book can be read for an independent study, used as a text for a two-semester course, or as a self-contained reference for the researcher.
Download or read book Encyclopedic Dictionary of Mathematics written by Nihon Sūgakkai and published by MIT Press. This book was released on 1993 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: V.1. A.N. v.2. O.Z. Apendices and indexes.
Download or read book Matrix and Operator Equations and Applications written by Mohammad Sal Moslehian and published by Springer Nature. This book was released on 2023-07-29 with total page 763 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns matrix and operator equations that are widely applied in various disciplines of science to formulate challenging problems and solve them in a faithful way. The main aim of this contributed book is to study several important matrix and operator equalities and equations in a systematic and self-contained fashion. Some powerful methods have been used to investigate some significant equations in functional analysis, operator theory, matrix analysis, and numerous subjects in the last decades. The book is divided into two parts: (I) Matrix Equations and (II) Operator Equations. In the first part, the state-of-the-art of systems of matrix equations is given and generalized inverses are used to find their solutions. The semi-tensor product of matrices is used to solve quaternion matrix equations. The contents of some chapters are related to the relationship between matrix inequalities, matrix means, numerical range, and matrix equations. In addition, quaternion algebras and their applications are employed in solving some famous matrix equations like Sylvester, Stein, and Lyapunov equations. A chapter devoted to studying Hermitian polynomial matrix equations, which frequently arise from linear-quadratic control problems. Moreover, some classical and recently discovered inequalities for matrix exponentials are reviewed. In the second part, the latest developments in solving several equations appearing in modern operator theory are demonstrated. These are of interest to a wide audience of pure and applied mathematicians. For example, the Daugavet equation in the linear and nonlinear setting, iterative processes and Volterra-Fredholm integral equations, semicircular elements induced by connected finite graphs, free probability, singular integral operators with shifts, and operator differential equations closely related to the properties of the coefficient operators in some equations are discussed. The chapters give a comprehensive account of their subjects. The exhibited chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.
Download or read book Control of Higher Dimensional PDEs written by Thomas Meurer and published by Springer Science & Business Media. This book was released on 2012-08-13 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents new model-based design methods for trajectory planning, feedback stabilization, state estimation, and tracking control of distributed-parameter systems governed by partial differential equations (PDEs). Flatness and backstepping techniques and their generalization to PDEs with higher-dimensional spatial domain lie at the core of this treatise. This includes the development of systematic late lumping design procedures and the deduction of semi-numerical approaches using suitable approximation methods. Theoretical developments are combined with both simulation examples and experimental results to bridge the gap between mathematical theory and control engineering practice in the rapidly evolving PDE control area. The text is divided into five parts featuring: - a literature survey of paradigms and control design methods for PDE systems - the first principle mathematical modeling of applications arising in heat and mass transfer, interconnected multi-agent systems, and piezo-actuated smart elastic structures - the generalization of flatness-based trajectory planning and feedforward control to parabolic and biharmonic PDE systems defined on general higher-dimensional domains - an extension of the backstepping approach to the feedback control and observer design for parabolic PDEs with parallelepiped domain and spatially and time varying parameters - the development of design techniques to realize exponentially stabilizing tracking control - the evaluation in simulations and experiments Control of Higher-Dimensional PDEs — Flatness and Backstepping Designs is an advanced research monograph for graduate students in applied mathematics, control theory, and related fields. The book may serve as a reference to recent developments for researchers and control engineers interested in the analysis and control of systems governed by PDEs.
Download or read book Functional Analysis written by Yurij M. Berezansky and published by Birkhäuser. This book was released on 2012-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional Analysis is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathemati- cal physics. The first volume reviews basic concepts such as the measure, the integral, Banach spaces, bounded operators and generalized functions. Volume II moves on to more ad- vanced topics including unbounded operators, spectral decomposition, expansion in generalized eigenvectors, rigged spaces, and partial differential operators. This text provides students of mathematics and physics with a clear introduction into the above concepts, with the theory well illustrated by a wealth of examples. Researchers will appreciate it as a useful reference manual.
