Introduction To Hilbert Spaces With Applications
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Author | : Lokenath Debnath |
Publisher | : Academic Press |
Total Pages | : 600 |
Release | : 2005-09-29 |
Genre | : Mathematics |
ISBN | : 0122084381 |
"Continuing 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 complemented by a variety of applications. Students and researchers will benefit from the enhanced presentation of results and proofs and new and revised examples. A completely new section on Sobolev spaces has been added, and the treatment of finite dimensional normed spaces has been expanded. The chapter on wavelets has been updated."--BOOK JACKET.
Author | : Lokenath Debnath |
Publisher | : Elsevier |
Total Pages | : 599 |
Release | : 2005-09-29 |
Genre | : Mathematics |
ISBN | : 0080455921 |
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
Author | : N. Young |
Publisher | : Cambridge University Press |
Total Pages | : 254 |
Release | : 1988-07-21 |
Genre | : Mathematics |
ISBN | : 1107717167 |
This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.
Author | : Lokenath Debnath |
Publisher | : Academic Press |
Total Pages | : 600 |
Release | : 2005-10-21 |
Genre | : |
ISBN | : 9781493300358 |
Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, 3E, 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 .
Author | : Samuel S. Holland |
Publisher | : Courier Corporation |
Total Pages | : 578 |
Release | : 2012-05-04 |
Genre | : Mathematics |
ISBN | : 0486139298 |
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.
Author | : W.-H. Steeb |
Publisher | : Springer Science & Business Media |
Total Pages | : 247 |
Release | : 2013-03-07 |
Genre | : Science |
ISBN | : 9401153329 |
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.
Author | : Sterling K. Berberian |
Publisher | : American Mathematical Soc. |
Total Pages | : 226 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 0821819127 |
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.''
Author | : Vern I. Paulsen |
Publisher | : Cambridge University Press |
Total Pages | : 193 |
Release | : 2016-04-11 |
Genre | : Mathematics |
ISBN | : 1107104092 |
A unique introduction to reproducing kernel Hilbert spaces, covering the fundamental underlying theory as well as a range of applications.
Author | : N. Young |
Publisher | : Cambridge University Press |
Total Pages | : 254 |
Release | : 1988-07-21 |
Genre | : Mathematics |
ISBN | : 9780521337175 |
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.
Author | : Edoardo Provenzi |
Publisher | : John Wiley & Sons |
Total Pages | : 370 |
Release | : 2021-08-24 |
Genre | : Mathematics |
ISBN | : 1786306824 |
From Euclidian to Hilbert Spaces analyzes the transition from finite dimensional Euclidian spaces to infinite-dimensional Hilbert spaces, a notion that can sometimes be difficult for non-specialists to grasp. The focus is on the parallels and differences between the properties of the finite and infinite dimensions, noting the fundamental importance of coherence between the algebraic and topological structure, which makes Hilbert spaces the infinite-dimensional objects most closely related to Euclidian spaces. The common thread of this book is the Fourier transform, which is examined starting from the discrete Fourier transform (DFT), along with its applications in signal and image processing, passing through the Fourier series and finishing with the use of the Fourier transform to solve differential equations. The geometric structure of Hilbert spaces and the most significant properties of bounded linear operators in these spaces are also covered extensively. The theorems are presented with detailed proofs as well as meticulously explained exercises and solutions, with the aim of illustrating the variety of applications of the theoretical results.