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Problems And Solutions In Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions And Quantum Mechanics

Author : Willi-hans Steeb

Publisher : World Scientific

Page : 454 pages

File Size : 40,58 MB

Release : 2022-08-23

Category : Mathematics

ISBN : 9811245746

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Book Description

This book presents a collection of problems and solutions in functional analysis with applications to quantum mechanics. Emphasis is given to Banach spaces, Hilbert spaces and generalized functions.The material of this volume is self-contained, whereby each chapter comprises an introduction with the relevant notations, definitions, and theorems. The approach in this volume is to provide students with instructive problems along with problem-solving strategies. Programming problems with solutions are also included.



Problems and Solutions in Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions and Quantum Mechanics

Author : Willi-Hans Steeb

Publisher : World Scientific Publishing Company

Page : 0 pages

File Size : 18,66 MB

Release : 2022-08

Category : Functional analysis

ISBN : 9789811246838

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Book Description

"This book summarizes the different topics in Functional Analysis with applications to Quantum Theory. It further includes Supplementary Problems and Programming Problems with Solutions"--



Introduction to Hilbert Spaces with Applications

Author : Lokenath Debnath

Publisher : Elsevier

Page : 599 pages

File Size : 24,73 MB

Release : 2005-09-29

Category : Mathematics

ISBN : 0080455921

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Book Description

Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory. - Updated chapter on wavelets - Improved presentation on results and proof - Revised examples and updated applications - Completely updated list of references



Problems And Solutions: Nonlinear Dynamics, Chaos And Fractals

Author : Willi-hans Steeb

Publisher : World Scientific Publishing Company

Page : 252 pages

File Size : 31,9 MB

Release : 2016-03-02

Category : Science

ISBN : 9813109947

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Book Description

This book presents a collection of problems for nonlinear dynamics, chaos theory and fractals. Besides the solved problems, supplementary problems are also added. Each chapter contains an introduction with suitable definitions and explanations to tackle the problems.The material is self-contained, and the topics range in difficulty from elementary to advanced. While students can learn important principles and strategies required for problem solving, lecturers will also find this text useful, either as a supplement or text, since concepts and techniques are developed in the problems.



Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics

Author : W.-H. Steeb

Publisher : Springer Science & Business Media

Page : 247 pages

File Size : 17,66 MB

Release : 2013-03-07

Category : Science

ISBN : 9401153329

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Book Description

This book gives a comprehensive introduction to modern quantum mechanics, emphasising the underlying Hilbert space theory and generalised function theory. All the major modern techniques and approaches used in quantum mechanics are introduced, such as Berry phase, coherent and squeezed states, quantum computing, solitons and quantum mechanics. Audience: The book is suitable for graduate students in physics and mathematics.



Applied Analysis

Author : John K. Hunter

Publisher : World Scientific

Page : 460 pages

File Size : 49,17 MB

Release : 2001

Category : Mathematics

ISBN : 9789810241919

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Book Description

This book provides an introduction to those parts of analysis that are most useful in applications for graduate students. The material is selected for use in applied problems, and is presented clearly and simply but without sacrificing mathematical rigor. The text is accessible to students from a wide variety of backgrounds, including undergraduate students entering applied mathematics from non-mathematical fields and graduate students in the sciences and engineering who want to learn analysis. A basic background in calculus, linear algebra and ordinary differential equations, as well as some familiarity with functions and sets, should be sufficient.



A Wavelet Tour of Signal Processing

Author : Stephane Mallat

Publisher : Elsevier

Page : 663 pages

File Size : 47,90 MB

Release : 1999-09-14

Category : Computers

ISBN : 0080520839

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Book Description

This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and ÉcolePolytechnique in Paris. - Provides a broad perspective on the principles and applications of transient signal processing with wavelets - Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms - Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements - Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet - Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition - Optical flow calculation and video compression algorithms - Image models with bounded variation functions - Bayes and Minimax theories for signal estimation - 200 pages rewritten and most illustrations redrawn - More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics



A Basis Theory Primer

Author : Christopher Heil

Publisher : Springer Science & Business Media

Page : 549 pages

File Size : 24,36 MB

Release : 2011

Category : Mathematics

ISBN : 0817646868

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Book Description

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.



A Guide to Distribution Theory and Fourier Transforms

Author : Robert S. Strichartz

Publisher : World Scientific

Page : 238 pages

File Size : 12,90 MB

Release : 2003

Category : Mathematics

ISBN : 9789812384300

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Book Description

This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.



Partial Inner Product Spaces

Author : J-P Antoine

Publisher : Springer

Page : 371 pages

File Size : 42,42 MB

Release : 2009-12-08

Category : Mathematics

ISBN : 3642051367

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Book Description

Partial Inner Product (PIP) Spaces are ubiquitous, e.g. Rigged Hilbert spaces, chains of Hilbert or Banach spaces (such as the Lebesgue spaces Lp over the real line), etc. In fact, most functional spaces used in (quantum) physics and in signal processing are of this type. The book contains a systematic analysis of PIP spaces and operators defined on them. Numerous examples are described in detail and a large bibliography is provided. Finally, the last chapters cover the many applications of PIP spaces in physics and in signal/image processing, respectively. As such, the book will be useful both for researchers in mathematics and practitioners of these disciplines.