Linear Operators And Their Spectra PDF Download
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Author | : E. Brian Davies |
Publisher | : Cambridge University Press |
Total Pages | : 436 |
Release | : 2007-04-26 |
Genre | : Mathematics |
ISBN | : 1139464337 |
Download Linear Operators and their Spectra Book in PDF, ePub and Kindle
This wide ranging but self-contained account of the spectral theory of non-self-adjoint linear operators is ideal for postgraduate students and researchers, and contains many illustrative examples and exercises. Fredholm theory, Hilbert-Schmidt and trace class operators are discussed, as are one-parameter semigroups and perturbations of their generators. Two chapters are devoted to using these tools to analyze Markov semigroups. The text also provides a thorough account of the new theory of pseudospectra, and presents the recent analysis by the author and Barry Simon of the form of the pseudospectra at the boundary of the numerical range. This was a key ingredient in the determination of properties of the zeros of certain orthogonal polynomials on the unit circle. Finally, two methods, both very recent, for obtaining bounds on the eigenvalues of non-self-adjoint Schrodinger operators are described. The text concludes with a description of the surprising spectral properties of the non-self-adjoint harmonic oscillator.
Author | : Vladimir Müller |
Publisher | : Springer Science & Business Media |
Total Pages | : 439 |
Release | : 2007-12-24 |
Genre | : Mathematics |
ISBN | : 3764382651 |
Download Spectral Theory of Linear Operators Book in PDF, ePub and Kindle
This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. Many results appear here for the first time in a monograph.
Author | : Edward Brian Davies |
Publisher | : |
Total Pages | : 451 |
Release | : 2007 |
Genre | : Linear operators |
ISBN | : 9780511285790 |
Download Linear Operators and Their Spectra Book in PDF, ePub and Kindle
Authoritative text presenting a broad view of the spectral theory of non-self-adjoint linear operators.
Author | : Edward Brian Davies |
Publisher | : |
Total Pages | : 451 |
Release | : 2007 |
Genre | : Electronic books |
ISBN | : 9781107170285 |
Download Linear Operators and Their Spectra Book in PDF, ePub and Kindle
Authoritative text presenting a broad view of the spectral theory of non-self-adjoint linear operators.
Author | : Aref Jeribi |
Publisher | : Springer |
Total Pages | : 599 |
Release | : 2015-07-04 |
Genre | : Science |
ISBN | : 3319175661 |
Download Spectral Theory and Applications of Linear Operators and Block Operator Matrices Book in PDF, ePub and Kindle
Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially-compact operators.
Author | : Henry R. Dowson |
Publisher | : |
Total Pages | : 444 |
Release | : 1978 |
Genre | : Banach spaces |
ISBN | : |
Download Spectral Theory of Linear Operators Book in PDF, ePub and Kindle
General spectral theory; Riesz operators; Hermitian operators; Prespectral operators; Well-bounded operators.
Author | : Israel Gohberg |
Publisher | : Birkhäuser |
Total Pages | : 291 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 1461259851 |
Download Basic Operator Theory Book in PDF, ePub and Kindle
rii application of linear operators on a Hilbert space. We begin with a chapter on the geometry of Hilbert space and then proceed to the spectral theory of compact self adjoint operators; operational calculus is next presented as a nat ural outgrowth of the spectral theory. The second part of the text concentrates on Banach spaces and linear operators acting on these spaces. It includes, for example, the three 'basic principles of linear analysis and the Riesz Fredholm theory of compact operators. Both parts contain plenty of applications. All chapters deal exclusively with linear problems, except for the last chapter which is an introduction to the theory of nonlinear operators. In addition to the standard topics in functional anal ysis, we have presented relatively recent results which appear, for example, in Chapter VII. In general, in writ ing this book, the authors were strongly influenced by re cent developments in operator theory which affected the choice of topics, proofs and exercises. One of the main features of this book is the large number of new exercises chosen to expand the reader's com prehension of the material, and to train him or her in the use of it. In the beginning portion of the book we offer a large selection of computational exercises; later, the proportion of exercises dealing with theoretical questions increases. We have, however, omitted exercises after Chap ters V, VII and XII due to the specialized nature of the subject matter.
Author | : Aref Jeribi |
Publisher | : CRC Press |
Total Pages | : 208 |
Release | : 2018-04-17 |
Genre | : Mathematics |
ISBN | : 135104625X |
Download Linear Operators and Their Essential Pseudospectra Book in PDF, ePub and Kindle
Linear Operators and Their Essential Pseudospectra provides a comprehensive study of spectral theory of linear operators defined on Banach spaces. The central items of interest in the volume include various essential spectra, but the author also considers some of the generalizations that have been studied. In recent years, spectral theory has witnessed an explosive development. This volume presents a survey of results concerning various types of essential spectra and pseudospectra in a unified, axiomatic way and also discusses several topics that are new but which relate to the concepts and methods emanating from the book. The main topics include essential spectra, essential pseudospectra, structured essential pseudospectra, and their relative sets. This volume will be very useful for several researchers since it represents not only a collection of previously heterogeneous material but also includes discussions of innovation through several extensions. As the spectral theory of operators is an important part of functional analysis and has numerous applications in many areas of mathematics, the author suggests that some modest prerequisites from functional analysis and operator theory should be in place to be accessible to newcomers and graduate students of mathematics.
Author | : Bernard Helffer |
Publisher | : Cambridge University Press |
Total Pages | : 263 |
Release | : 2013-01-17 |
Genre | : Mathematics |
ISBN | : 110703230X |
Download Spectral Theory and Its Applications Book in PDF, ePub and Kindle
Introduces the basic tools in spectral analysis using numerous examples from the Schrödinger operator theory and various branches of physics.
Author | : Michael Gil' |
Publisher | : CRC Press |
Total Pages | : 224 |
Release | : 2017-03-03 |
Genre | : Mathematics |
ISBN | : 1498796915 |
Download Bounds for Determinants of Linear Operators and their Applications Book in PDF, ePub and Kindle
This book deals with the determinants of linear operators in Euclidean, Hilbert and Banach spaces. Determinants of operators give us an important tool for solving linear equations and invertibility conditions for linear operators, enable us to describe the spectra, to evaluate the multiplicities of eigenvalues, etc. We derive upper and lower bounds, and perturbation results for determinants, and discuss applications of our theoretical results to spectrum perturbations, matrix equations, two parameter eigenvalue problems, as well as to differential, difference and functional-differential equations.