Download or read book A Primer on Hilbert Space Theory written by Carlo Alabiso and published by Springer Nature. This book was released on 2021-03-03 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors’s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.
Download or read book A Primer on Hilbert Space Operators written by Piotr Sołtan and published by Springer. This book was released on 2018-09-04 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book concisely presents the fundamental aspects of the theory of operators on Hilbert spaces. The topics covered include functional calculus and spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter groups of operators. The exposition of the material on unbounded operators is based on a novel tool, called the z-transform, which provides a way to encode full information about unbounded operators in bounded ones, hence making many technical aspects of the theory less involved.
Download or read book A Primer of Hilbert Space written by Claudi Meneghin and published by . This book was released on 2013 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operators on Hilbert Space written by V. S. Sunder and published by Springer. This book was released on 2016-08-05 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators.
Download or read book An Introduction to Hilbert Space written by N. Young and published by Cambridge University Press. This book was released on 1988-07-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of a Hilbert space is a central idea in functional analysis and this text demonstrates its applications in numerous branches of pure and applied mathematics.
Download or read book A Primer on Reproducing Kernel Hilbert Spaces written by Jonathan H. Manton and published by . This book was released on 2015-11-20 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert space theory is an invaluable mathematical tool in numerous signal processing and systems theory applications. Hilbert spaces satisfying certain additional properties are known as Reproducing Kernel Hilbert Spaces (RKHSs). This primer gives a gentle and novel introduction to RKHS theory. It also presents several classical applications. It concludes by focusing on recent developments in the machine learning literature concerning embeddings of random variables. Parenthetical remarks are used to provide greater technical detail, which some readers may welcome, but they may be ignored without compromising the cohesion of the primer. Proofs are there for those wishing to gain experience at working with RKHSs; simple proofs are preferred to short, clever, but otherwise uninformative proofs. Italicised comments appearing in proofs provide intuition or orientation or both. A Primer on Reproducing Kernel Hilbert Spaces empowers readers to recognize when and how RKHS theory can profit them in their own work.
Download or read book Hilbert Space Methods in Signal Processing written by Rodney A. Kennedy and published by Cambridge University Press. This book was released on 2013-03-07 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to Hilbert spaces, combining the theory with applications of Hilbert methods in signal processing.
Download or read book Introduction to Hilbert Space written by Sterling K. Berberian and published by American Mathematical Soc.. This book was released on 1999 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface: ``This textbook has evolved from a set of lecture notes ... In both the course and the book, I have in mind first- or second-year graduate students in Mathematics and related fields such as Physics ... It is necessary for the reader to have a foundation in advanced calculus which includes familiarity with: least upper bound (LUB) and greatest lower bound (GLB), the concept of function, $\epsilon$'s and their companion $\delta$'s, and basic properties of sequences of real and complex numbers (convergence, Cauchy's criterion, the Weierstrass-Bolzano theorem). It is not presupposed that the reader is acquainted with vector spaces ... , matrices ... , or determinants ... There are over four hundred exercises, most of them easy ... It is my hope that this book, aside from being an exposition of certain basic material on Hilbert space, may also serve as an introduction to other areas of functional analysis.''
Download or read book Convex Analysis and Monotone Operator Theory in Hilbert Spaces written by Heinz H. Bauschke and published by Springer. This book was released on 2017-02-28 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated. Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada. Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.
Download or read book A Basis Theory Primer written by Christopher Heil and published by Springer Science & Business Media. This book was released on 2011 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses. The self-contained presentation with clear proofs is accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications.
Download or read book A Primer on the Dirichlet Space written by Omar El-Fallah and published by Cambridge University Press. This book was released on 2014-01-16 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic account of the Dirichlet space, assembling results previously only found in scattered research articles, and improving upon many of the proofs. Topics treated include: the Douglas and Carleson formulas for the Dirichlet integral, reproducing kernels, boundary behaviour and capacity, zero sets and uniqueness sets, multipliers, interpolation, Carleson measures, composition operators, local Dirichlet spaces, shift-invariant subspaces, and cyclicity. Special features include a self-contained treatment of capacity, including the strong-type inequality. The book will be valuable to researchers in function theory, and with over 100 exercises it is also suitable for self-study by graduate students.
Download or read book Hilbert Spaces and Operator Theory written by W. Mlak and published by Springer. This book was released on 1991-11-30 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizing a clear exposition for readers familiar with elementary measure theory and the fundamentals of set theory and general topology, presents the basic notions and methods of the theory of Hilbert spaces, a part of functional analysis being increasingly applied in mathematics and theoretical
Download or read book A Mathematical Primer on Quantum Mechanics written by Alessandro Teta and published by Springer. This book was released on 2018-04-17 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.
Download or read book Hilbert Space Operators written by Carlos S. Kubrusly and published by Springer Science & Business Media. This book was released on 2003-08-07 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained work on Hilbert space operators takes a problem-solving approach to the subject, combining theoretical results with a wide variety of exercises that range from the straightforward to the state-of-the-art. Complete solutions to all problems are provided. The text covers the basics of bounded linear operators on a Hilbert space and gradually progresses to more advanced topics in spectral theory and quasireducible operators. Written in a motivating and rigorous style, the work has few prerequisites beyond elementary functional analysis, and will appeal to graduate students and researchers in mathematics, physics, engineering, and related disciplines.
Download or read book A Primer for a Secret Shortcut to PDEs of Mathematical Physics written by Des McGhee and published by Springer Nature. This book was released on 2020-08-24 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise introduction to a unified Hilbert space approach to the mathematical modelling of physical phenomena which has been developed over recent years by Picard and his co-workers. The main focus is on time-dependent partial differential equations with a particular structure in the Hilbert space setting that ensures well-posedness and causality, two essential properties of any reasonable model in mathematical physics or engineering.However, the application of the theory to other types of equations is also demonstrated. By means of illustrative examples, from the straightforward to the more complex, the authors show that many of the classical models in mathematical physics as well as more recent models of novel materials and interactions are covered, or can be restructured to be covered, by this unified Hilbert space approach. The reader should require only a basic foundation in the theory of Hilbert spaces and operators therein. For convenience, however, some of the more technical background requirements are covered in detail in two appendices The theory is kept as elementary as possible, making the material suitable for a senior undergraduate or master’s level course. In addition, researchers in a variety of fields whose work involves partial differential equations and applied operator theory will also greatly benefit from this approach to structuring their mathematical models in order that the general theory can be applied to ensure the essential properties of well-posedness and causality.
Download or read book A Hilbert Space Problem Book written by P.R. Halmos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."
Download or read book Hilbert Space Methods in Science and Engineering written by László Máté and published by CRC Press. This book was released on 1990 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume aims to present Hilbert space theory as an accessible language for applied mathematicians, engineers and scientists. A knowledge of linear algebra and analysis is assumed. The construction of mathematical models using Hilbert space theory is illustrated with problems and results are evaluated. For the first time, mathematical models based on reproducing kernel Hilbert spaces and causal operators are explained at an introductory level.
