Linear Operators In Hilbert Space

Author : Joachim Weidmann
Publisher : Springer Science & Business Media
Page : 413 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461260271

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Linear Operators in Hilbert Spaces by Joachim Weidmann Pdf

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 : V. S. Sunder
Publisher : Springer
Page : 100 pages
File Size : 52,9 Mb
Release : 2016-08-05
Category : Mathematics
ISBN : 9789811018169

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Operators on Hilbert Space by V. S. Sunder Pdf

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.

Author : Jean Louis Soulé
Publisher : CRC Press
Page : 60 pages
File Size : 43,6 Mb
Release : 1968
Category : Mathematics
ISBN : 0677301758

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Linear Operators in Hilbert Space by Jean Louis Soulé Pdf

Author : Takayuki Furuta
Publisher : CRC Press
Page : 276 pages
File Size : 50,5 Mb
Release : 2001-07-26
Category : Mathematics
ISBN : 0415267994

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Invitation to Linear Operators by Takayuki Furuta Pdf

Most books on linear operators are not easy to follow for students and researchers without an extensive background in mathematics. Self-contained and using only matrix theory, Invitation to Linear Operators: From Matricies to Bounded Linear Operators on a Hilbert Space explains in easy-to-follow steps a variety of interesting recent results on linear operators on a Hilbert space. The author first states the important properties of a Hilbert space, then sets out the fundamental properties of bounded linear operators on a Hilbert space. The final section presents some of the more recent developments in bounded linear operators.

Author : Harkrishan Lal Vasudeva
Publisher : Springer
Page : 522 pages
File Size : 47,7 Mb
Release : 2017-03-27
Category : Mathematics
ISBN : 9789811030208

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Elements of Hilbert Spaces and Operator Theory by Harkrishan Lal Vasudeva Pdf

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 : N. I. Akhiezer,I. M. Glazman
Publisher : Courier Corporation
Page : 378 pages
File Size : 55,8 Mb
Release : 2013-04-15
Category : Mathematics
ISBN : 9780486318653

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Theory of Linear Operators in Hilbert Space by N. I. Akhiezer,I. M. Glazman Pdf

This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.

Author : Werner Schmeidler
Publisher : Unknown
Page : 140 pages
File Size : 40,5 Mb
Release : 1965
Category : Algebras, Linear
ISBN : UOM:39015053609106

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Linear Operators in Hilbert Space by Werner Schmeidler Pdf

Author : Naum Il'ič Ahiezer
Publisher : Unknown
Page : 218 pages
File Size : 53,9 Mb
Release : 1993
Category : Electronic
ISBN : OCLC:910023421

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Theory of Linear Operators in Hilbert Space by Naum Il'ič Ahiezer Pdf

Author : Silvestru Sever Dragomir
Publisher : Springer Science & Business Media
Page : 130 pages
File Size : 51,7 Mb
Release : 2013-09-14
Category : Mathematics
ISBN : 9783319014487

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Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces by Silvestru Sever Dragomir Pdf

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 : Michael Sh. Birman,M.Z. Solomjak
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400945869

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Spectral Theory of Self-Adjoint Operators in Hilbert Space by Michael Sh. Birman,M.Z. Solomjak Pdf

It isn't that they can't see the solution. It is Approach your problems from the right end that they can't see the problem. and begin with the answers. Then one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be com pletely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order" , which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Author : Paul A. Fuhrmann
Publisher : Courier Corporation
Page : 340 pages
File Size : 51,9 Mb
Release : 2014-01-15
Category : Mathematics
ISBN : 9780486782263

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Linear Systems and Operators in Hilbert Space by Paul A. Fuhrmann Pdf

Three-part approach, with notes and references for each section, covers linear algebra and finite dimensional systems, operators in Hilbert space, and linear systems in Hilbert space. 1981 edition.

Author : Carlos S. Kubrusly
Publisher : Springer Science & Business Media
Page : 162 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220640

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Hilbert Space Operators by Carlos S. Kubrusly Pdf

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 : Fazlollah M. Reza
Publisher : Unknown
Page : 100 pages
File Size : 52,7 Mb
Release : 1968
Category : Hilbert space
ISBN : UOM:39015049076386

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An Exposition of Hilbert Space and Linear Operators for Engineers and Scientists by Fazlollah M. Reza Pdf

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 : Tosio Kato
Publisher : Springer Science & Business Media
Page : 610 pages
File Size : 42,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662126783

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Perturbation theory for linear operators by Tosio Kato Pdf

Author : Naum I. Achiezer
Publisher : Unknown
Page : 128 pages
File Size : 51,7 Mb
Release : 1981
Category : Electronic
ISBN : OCLC:630852082

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Theory of Linear Operators in Hilbert Space by Naum I. Achiezer Pdf