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

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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
ISBN 13 : 9811245746
Total Pages : 454 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Problems And Solutions In Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions And Quantum Mechanics by : Willi-hans Steeb

Download or read book Problems And Solutions In Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions And Quantum Mechanics written by Willi-hans Steeb and published by World Scientific. This book was released on 2022-08-23 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. MATHIS STEEB (WOLFGANG.)
Publisher : World Scientific Publishing Company
ISBN 13 : 9789811245725
Total Pages : 0 pages
Book Rating : 4.2/5 (457 download)

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Book Synopsis Problems and Solutions in Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions and Quantum Mechanics by : WILLI-HANS. MATHIS STEEB (WOLFGANG.)

Download or read book Problems and Solutions in Banach Spaces, Hilbert Spaces, Fourier Transform, Wavelets, Generalized Functions and Quantum Mechanics written by WILLI-HANS. MATHIS STEEB (WOLFGANG.) and published by World Scientific Publishing Company. This book was released on 2022-09-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Hilbert Spaces, Generalized Functions and Quantum Mechanics

Author : Willi-Hans Steeb
Publisher :
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Hilbert Spaces, Generalized Functions and Quantum Mechanics by : Willi-Hans Steeb

Download or read book Hilbert Spaces, Generalized Functions and Quantum Mechanics written by Willi-Hans Steeb and published by . This book was released on 1991 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Primer on Hilbert Space Theory

Author : Carlo Alabiso
Publisher : Springer Nature
ISBN 13 : 3030674177
Total Pages : 343 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis A Primer on Hilbert Space Theory by : Carlo Alabiso

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.

Hilbert Spaces

Author :
Publisher : Elsevier
ISBN 13 : 008052835X
Total Pages : 597 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Hilbert Spaces by :

Download or read book Hilbert Spaces written by and published by Elsevier. This book was released on 2001-07-11 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has evolved from the lecture course on Functional Analysis I had given several times at the ETH. The text has a strict logical order, in the style of “Definition – Theorem – Proof - Example - Exercises . The proofs are rather thorough and there many examples. The first part of the book(the first three chapters, resp. the first two volumes) is devoted to the theory of Banach spaces in the most general sense of the term. The purpose of the first chapter (resp. first volume) is to introduce those results on Banach spaces which are used later or which are closely connected with the book. It therefore only contains a small part of the theory, and several results are stated (and proved) in a diluted form. The second chapter (which together with Chapter 3 makes the second volume) deals with Banach algebras (and involutive Banach algebras), which constitute the main topic of the first part of the book. The third chapter deals with compact operators on Banach spaces and linear (ordinary and partial) differential equations - applications of the, theory of Banach algebras.

A Hilbert Space Problem Book

Author : P.R. Halmos
Publisher : Springer Science & Business Media
ISBN 13 : 1461599768
Total Pages : 377 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis A Hilbert Space Problem Book by : P.R. Halmos

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 377 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."

Hilbert Space Operators

Author : Carlos S. Kubrusly
Publisher : Springer Science & Business Media
ISBN 13 : 1461220645
Total Pages : 162 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Hilbert Space Operators by : Carlos S. Kubrusly

Download or read book Hilbert Space Operators written by Carlos S. Kubrusly and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 162 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.

An Introduction to Hilbert Space

Author : N. Young
Publisher : Cambridge University Press
ISBN 13 : 9780521337175
Total Pages : 254 pages
Book Rating : 4.3/5 (371 download)

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Book Synopsis An Introduction to Hilbert Space by : N. Young

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.

Spectral Theory of Operators in Hilbert Space

Author : Kurt Otto Friedrichs
Publisher :
ISBN 13 : 9781258449834
Total Pages : 218 pages
Book Rating : 4.4/5 (498 download)

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Book Synopsis Spectral Theory of Operators in Hilbert Space by : Kurt Otto Friedrichs

Download or read book Spectral Theory of Operators in Hilbert Space written by Kurt Otto Friedrichs and published by . This book was released on 2012-07-01 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Present Lectures Intend To Provide An Introduction To The Spectral Analysis Of Self-Joint Operators Within The Framework Of Hilbert Space Theory. The Guiding Notion In This Approach Is That Of Spectral Representation. At The Same Time The Notion Of Function Of An Operator Is Emphasized. The Definition Of Hilbert Space: In Mathematics, A Hilbert Space Is A Real Or Complex Vector Space With A Positive-Definite Hermitian Form, That Is Complete Under Its Norm. Thus It Is An Inner Product Space, Which Means That It Has Notions Of Distance And Of Angle (Especially The Notion Of Orthogonality Or Perpendicularity). The Completeness Requirement Ensures That For Infinite Dimensional Hilbert Spaces The Limits Exist When Expected, Which Facilitates Various Definitions From Calculus. A Typical Example Of A Hilbert Space Is The Space Of Square Summable Sequences. Hilbert Spaces Allow Simple Geometric Concepts, Like Projection And Change Of Basis To Be Applied To Infinite Dimensional Spaces, Such As Function Spaces. They Provide A Context With Which To Formalize And Generalize The Concepts Of The Fourier Series In Terms Of Arbitrary Orthogonal Polynomials And Of The Fourier Transform, Which Are Central Concepts From Functional Analysis. Hilbert Spaces Are Of Crucial Importance In The Mathematical Formulation Of Quantum Mechanics.

Hilbert Spaces and Its Applications

Author : Michael Argyros
Publisher :
ISBN 13 : 9781536189834
Total Pages : 0 pages
Book Rating : 4.1/5 (898 download)

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Book Synopsis Hilbert Spaces and Its Applications by : Michael Argyros

Download or read book Hilbert Spaces and Its Applications written by Michael Argyros and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains numerous selected contemporary topics, primarily in Hilbert space, although related extended material in Banach spaces and Riemannian manifolds is also included. A plethora of concrete problems from diverse disciplines are explored, such as: applied mathematics; mathematical biology; chemistry; economics; physics; scientific computing, and engineering. The solutions of such equations can only be found in closed form in special cases; this forces researchers and practitioners to focus on the development of iterative methods to generate a sequence converging to the solutions, provided that some convergence criteria depending on the initial data are satisfied. Due to the exponential development of technology, new iterative methods should be found to improve existing computers and create faster and more efficient ones. We have no doubt that this book will contribute significantly to the enrichment of knowledge and problem solving in the field of Hilbert spaces and related topics.

The Theory of H(b) Spaces: Volume 1

Author : Emmanuel Fricain
Publisher : Cambridge University Press
ISBN 13 : 1316060918
Total Pages : 703 pages
Book Rating : 4.3/5 (16 download)

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Book Synopsis The Theory of H(b) Spaces: Volume 1 by : Emmanuel Fricain

Download or read book The Theory of H(b) Spaces: Volume 1 written by Emmanuel Fricain and published by Cambridge University Press. This book was released on 2016-05-26 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: An H(b) space is defined as a collection of analytic functions which are in the image of an operator. The theory of H(b) spaces bridges two classical subjects: complex analysis and operator theory, which makes it both appealing and demanding. The first volume of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators, and Clark measures. The second volume focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.

Applied Analysis by the Hilbert Space Method

Author : Samuel S. Holland
Publisher : Courier Corporation
ISBN 13 : 0486139298
Total Pages : 578 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Applied Analysis by the Hilbert Space Method by : Samuel S. Holland

Download or read book Applied Analysis by the Hilbert Space Method written by Samuel S. Holland and published by Courier Corporation. This book was released on 2012-05-04 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous worked examples and exercises highlight this unified treatment. Simple explanations of difficult subjects make it accessible to undergraduates as well as an ideal self-study guide. 1990 edition.

Hilbert Space Methods in Partial Differential Equations

Author : Ralph E. Showalter
Publisher : Courier Corporation
ISBN 13 : 0486135799
Total Pages : 226 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Hilbert Space Methods in Partial Differential Equations by : Ralph E. Showalter

Download or read book Hilbert Space Methods in Partial Differential Equations written by Ralph E. Showalter and published by Courier Corporation. This book was released on 2011-09-12 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.

Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces

Author : Joram Lindenstrauss
Publisher : Princeton University Press
ISBN 13 : 1400842697
Total Pages : 436 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces by : Joram Lindenstrauss

Download or read book Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces written by Joram Lindenstrauss and published by Princeton University Press. This book was released on 2012-02-26 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis. The new methods developed here include a game approach to perturbational variational principles that is of independent interest. Detailed explanation of the underlying ideas and motivation behind the proofs of the new results on Fréchet differentiability of vector-valued functions should make these arguments accessible to a wider audience. The most important special case of the differentiability results, that Lipschitz mappings from a Hilbert space into the plane have points of Fréchet differentiability, is given its own chapter with a proof that is independent of much of the work done to prove more general results. The book raises several open questions concerning its two main topics.

Elements of Hilbert Spaces and Operator Theory

Author : Harkrishan Lal Vasudeva
Publisher : Springer
ISBN 13 : 9811030200
Total Pages : 528 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Elements of Hilbert Spaces and Operator Theory by : Harkrishan Lal Vasudeva

Download or read book Elements of Hilbert Spaces and Operator Theory written by Harkrishan Lal Vasudeva and published by Springer. This book was released on 2017-03-27 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compression spectrum, have been worked out. Spectral theorems for self-adjoint operators, and normal operators, follow the spectral theorem for compact normal operators. The book also discusses invariant subspaces with special attention to the Volterra operator and unbounded operators. In order to make the text as accessible as possible, motivation for the topics is introduced and a greater amount of explanation than is usually found in standard texts on the subject is provided. The abstract theory in the book is supplemented with concrete examples. It is expected that these features will help the reader get a good grasp of the topics discussed. Hints and solutions to all the problems are collected at the end of the book. Additional features are introduced in the book when it becomes imperative. This spirit is kept alive throughout the book.

Pick Interpolation and Hilbert Function Spaces

Author : Jim Agler
Publisher : American Mathematical Soc.
ISBN 13 : 9780821883907
Total Pages : 332 pages
Book Rating : 4.8/5 (839 download)

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Book Synopsis Pick Interpolation and Hilbert Function Spaces by : Jim Agler

Download or read book Pick Interpolation and Hilbert Function Spaces written by Jim Agler and published by American Mathematical Soc.. This book was released on 2002 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $Hinfty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $Hinfty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider theinterpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem,and the hereditary functional calculus.

Hilbert Space Methods in Science and Engineering,

Author : László Máté
Publisher : CRC Press
ISBN 13 :
Total Pages : 292 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Hilbert Space Methods in Science and Engineering, by : László Máté

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.