An Exposition Of Hilbert Space And Linear Operators For Engineers And Scientists
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| Author | : Fazlollah M. Reza |
| Publisher | : |
| Total Pages | : 100 |
| Release | : 1968 |
| Genre | : Hilbert space |
| ISBN | : |
The vast and rapid advancement in telecommunications, computers, controls, and aerospace science has necessitated major changes in our basic understanding of the theory of electrical signals and processing systems. There is strong evidence that today's engineer needs to extend and to modernize his analytical techniques. The latest fundamental analytical approach for the study of signals and systems seems to have its roots in the mathematics of Functional Analysis. This report contains a bird's-eye view of the elements of Hilbert spaces and their associated linear operators. The first chapter of the report gives an exposition of the most essential properties of Hilbert spaces. The second chapter presents the elements of linear operators acting on such spaces. The report is addressed to engineers and scientists interested in the theory of signals and systems. The applications of the theory will be undertaken in a separate report. (Author).
| Author | : Joachim Weidmann |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 413 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461260272 |
This English edition is almost identical to the German original Lineare Operatoren in Hilbertriiumen, published by B. G. Teubner, Stuttgart in 1976. A few proofs have been simplified, some additional exercises have been included, and a small number of new results has been added (e.g., Theorem 11.11 and Theorem 11.23). In addition a great number of minor errors has been corrected. Frankfurt, January 1980 J. Weidmann vii Preface to the German edition The purpose of this book is to give an introduction to the theory of linear operators on Hilbert spaces and then to proceed to the interesting applica tions of differential operators to mathematical physics. Besides the usual introductory courses common to both mathematicians and physicists, only a fundamental knowledge of complex analysis and of ordinary differential equations is assumed. The most important results of Lebesgue integration theory, to the extent that they are used in this book, are compiled with complete proofs in Appendix A. I hope therefore that students from the fourth semester on will be able to read this book without major difficulty. However, it might also be of some interest and use to the teaching and research mathematician or physicist, since among other things it makes easily accessible several new results of the spectral theory of differential operators.
| Author | : Carlos S. Kubrusly |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 162 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461220645 |
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.
| Author | : László Máté |
| Publisher | : CRC Press |
| Total Pages | : 292 |
| Release | : 1990 |
| Genre | : Art |
| ISBN | : |
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.
| Author | : Arch W. Naylor |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 648 |
| Release | : 1982 |
| Genre | : Mathematics |
| ISBN | : 9780387950013 |
This book is a unique introduction to the theory of linear operators on Hilbert space. The authors' goal is to present the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. First published in 1971, Linear Operator in Engineering and Sciences has since proved to be a popular and very useful textbook.
| Author | : H. Ted Davis |
| Publisher | : Elsevier |
| Total Pages | : 561 |
| Release | : 2000-07-12 |
| Genre | : Mathematics |
| ISBN | : 0080510248 |
Designed for advanced engineering, physical science, and applied mathematics students, this innovative textbook is an introduction to both the theory and practical application of linear algebra and functional analysis. The book is self-contained, beginning with elementary principles, basic concepts, and definitions. The important theorems of the subject are covered and effective application tools are developed, working up to a thorough treatment of eigenanalysis and the spectral resolution theorem. Building on a fundamental understanding of finite vector spaces, infinite dimensional Hilbert spaces are introduced from analogy. Wherever possible, theorems and definitions from matrix theory are called upon to drive the analogy home. The result is a clear and intuitive segue to functional analysis, culminating in a practical introduction to the functional theory of integral and differential operators. Numerous examples, problems, and illustrations highlight applications from all over engineering and the physical sciences. Also included are several numerical applications, complete with Mathematica solutions and code, giving the student a "hands-on" introduction to numerical analysis. Linear Algebra and Linear Operators in Engineering is ideally suited as the main text of an introductory graduate course, and is a fine instrument for self-study or as a general reference for those applying mathematics. Contains numerous Mathematica examples complete with full code and solutions Provides complete numerical algorithms for solving linear and nonlinear problems Spans elementary notions to the functional theory of linear integral and differential equations Includes over 130 examples, illustrations, and exercises and over 220 problems ranging from basic concepts to challenging applications Presents real-life applications from chemical, mechanical, and electrical engineering and the physical sciences
| Author | : Silvestru Sever Dragomir |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 130 |
| Release | : 2013-09-14 |
| Genre | : Mathematics |
| ISBN | : 331901448X |
Aimed toward researchers, postgraduate students, and scientists in linear operator theory and mathematical inequalities, this self-contained monograph focuses on numerical radius inequalities for bounded linear operators on complex Hilbert spaces for the case of one and two operators. Students at the graduate level will learn some essentials that may be useful for reference in courses in functional analysis, operator theory, differential equations, and quantum computation, to name several. Chapter 1 presents fundamental facts about the numerical range and the numerical radius of bounded linear operators in Hilbert spaces. Chapter 2 illustrates recent results obtained concerning numerical radius and norm inequalities for one operator on a complex Hilbert space, as well as some special vector inequalities in inner product spaces due to Buzano, Goldstein, Ryff and Clarke as well as some reverse Schwarz inequalities and Grüss type inequalities obtained by the author. Chapter 3 presents recent results regarding the norms and the numerical radii of two bounded linear operators. The techniques shown in this chapter are elementary but elegant and may be accessible to undergraduate students with a working knowledge of operator theory. A number of vector inequalities in inner product spaces as well as inequalities for means of nonnegative real numbers are also employed in this chapter. All the results presented are completely proved and the original references are mentioned.
| Author | : Harkrishan Lal Vasudeva |
| Publisher | : Springer |
| Total Pages | : 528 |
| Release | : 2017-03-27 |
| Genre | : Mathematics |
| ISBN | : 9811030200 |
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.
| Author | : Carlo Alabiso |
| Publisher | : Springer Nature |
| Total Pages | : 343 |
| Release | : 2021-03-03 |
| Genre | : Science |
| ISBN | : 3030674177 |
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.
| Author | : Jean Louis Soulé |
| Publisher | : CRC Press |
| Total Pages | : 60 |
| Release | : 1968 |
| Genre | : Mathematics |
| ISBN | : 9780677301754 |
