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Operators on Hilbert Space

2016-08-05 Mathematics
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Release : 2016-08-05
Genre : Mathematics
Kind : eBook
Book Rating : 162/5 ( reviews)

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Book Synopsis Operators on Hilbert Space by : V. S. Sunder

Download or read book Operators on Hilbert Space written by V. S. Sunder. This book was released on 2016-08-05. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Unbounded Self-adjoint Operators on Hilbert Space

2012-07-09 Mathematics
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Release : 2012-07-09
Genre : Mathematics
Kind : eBook
Book Rating : 535/5 ( reviews)

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Book Synopsis Unbounded Self-adjoint Operators on Hilbert Space by : Konrad Schmüdgen

Download or read book Unbounded Self-adjoint Operators on Hilbert Space written by Konrad Schmüdgen. This book was released on 2012-07-09. Available in PDF, EPUB and Kindle. Book excerpt: The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises. The main themes of the book are the following: - Spectral integrals and spectral decompositions of self-adjoint and normal operators - Perturbations of self-adjointness and of spectra of self-adjoint operators - Forms and operators - Self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extension

Linear Operators in Hilbert Spaces

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 272/5 ( reviews)

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Book Synopsis Linear Operators in Hilbert Spaces by : Joachim Weidmann

Download or read book Linear Operators in Hilbert Spaces written by Joachim Weidmann. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Harmonic Analysis of Operators on Hilbert Space

2010-09-01 Mathematics
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Release : 2010-09-01
Genre : Mathematics
Kind : eBook
Book Rating : 937/5 ( reviews)

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Book Synopsis Harmonic Analysis of Operators on Hilbert Space by : Béla Sz Nagy

Download or read book Harmonic Analysis of Operators on Hilbert Space written by Béla Sz Nagy. This book was released on 2010-09-01. Available in PDF, EPUB and Kindle. Book excerpt: The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.

Elements of Hilbert Spaces and Operator Theory

2017-03-27 Mathematics
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Release : 2017-03-27
Genre : Mathematics
Kind : eBook
Book Rating : 200/5 ( reviews)

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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. This book was released on 2017-03-27. 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.

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