Numerical Ranges
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Numerical Ranges Of Operators On Normed Spaces And Of Elements Of Normed Algebras
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Author : F. F. Bonsall
language : en
Publisher: CUP Archive
Release Date : 1971-03-02
Numerical Ranges Of Operators On Normed Spaces And Of Elements Of Normed Algebras written by F. F. Bonsall and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-03-02 with Mathematics categories.
The authors develop various applications, in particular to the study of Banach algebras where the numerical range provides an important link between the algebraic and metric structures.
Numerical Range
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Author : Karl E. Gustafson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Range written by Karl E. Gustafson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more efficient expression, and because in recent conferences dedicated to W(T), even the linear algebra commu nity has adopted it. Also, one universally refers to the numerical radius, and not to the field of values radius. Originally, Toeplitz and Hausdorff called it the Wertvorrat of a bilinear form, so other good names would be value field or form values. The Russian community has referred to it as the Hausdorff domain. Murnaghan in his early paper first called it the region of the complex plane covered by those values for an n x n matrix T, then the range of values of a Hermitian matrix, then the field of values when he analyzed what he called the sought-for region.
Numerical Ranges Of Hilbert Space Operators
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Author : Hwa-Long Gau
language : en
Publisher: Cambridge University Press
Release Date : 2021-07-31
Numerical Ranges Of Hilbert Space Operators written by Hwa-Long Gau and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-31 with Mathematics categories.
Model Theory And Linear Extreme Points In The Numerical Radius Unit Ball
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Author : Michael A. Dritschel
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Model Theory And Linear Extreme Points In The Numerical Radius Unit Ball written by Michael A. Dritschel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
This memoir initiates a model theory-based study of the numerical radius norm. Guided by the abstract model theory of Jim Agler, the authors propose a decomposition for operators that is particularly useful in understanding their properties with respect to the numerical radius norm. Of the topics amenable to investigation with these tools, the following are presented: a complete description of the linear extreme points of the non-matrix (numerical radius) unit ball; several equivalent characterizations of matricial extremals in the unit ball, that is, those members which do not allow a nontrivial extension remaining in the unit ball; and applications to numerical ranges of matrices, including a complete parameterization of all matrices whose numerical ranges are closed disks.
Numerical Range
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Author : Karl E. Gustafson
language : en
Publisher: Springer
Release Date : 1996-11-07
Numerical Range written by Karl E. Gustafson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-07 with Mathematics categories.
The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more efficient expression, and because in recent conferences dedicated to W(T), even the linear algebra commu nity has adopted it. Also, one universally refers to the numerical radius, and not to the field of values radius. Originally, Toeplitz and Hausdorff called it the Wertvorrat of a bilinear form, so other good names would be value field or form values. The Russian community has referred to it as the Hausdorff domain. Murnaghan in his early paper first called it the region of the complex plane covered by those values for an n x n matrix T, then the range of values of a Hermitian matrix, then the field of values when he analyzed what he called the sought-for region.
Spectral Theory Of Block Operator Matrices And Applications
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Author : Christiane Tretter
language : en
Publisher: World Scientific
Release Date : 2008-10-15
Spectral Theory Of Block Operator Matrices And Applications written by Christiane Tretter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-15 with Mathematics categories.
This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices. Particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not readily apply: non-self-adjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics.The main topics include: localization of the spectrum by means of new concepts of numerical range; investigation of the essential spectrum; variational principles and eigenvalue estimates; block diagonalization and invariant subspaces; solutions of algebraic Riccati equations; applications to spectral problems from magnetohydrodynamics, fluid mechanics, and quantum mechanics./a
Distributed Applications And Interoperable Systems
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Author : Frank Eliassen
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-06
Distributed Applications And Interoperable Systems written by Frank Eliassen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-06 with Computers categories.
This book constitutes the refereed proceedings of the 6th IFIP WG 6.1 International Conference on Distributed Applications and Interoperable Systems, DAIS 2006, held in Bologna, Italy, June 2006. The book presents 21 revised regular and 5 revised work-in-progress papers, on architectures, models, technologies and platforms for interoperable, scalable and adaptable systems and cover subjects as methodological aspects, tools and language of building adaptable distributed and interoperable services, and many more.
Spectra And Pseudospectra
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Author : Lloyd N. Trefethen
language : en
Publisher: Princeton University Press
Release Date : 2020-05-05
Spectra And Pseudospectra written by Lloyd N. Trefethen and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-05 with Mathematics categories.
Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.
Nonlinear Spectral Theory
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Author : Jürgen Appell
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22
Nonlinear Spectral Theory written by Jürgen Appell and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.
In view of the eminent importance of spectral theory of linear operators in many fields of mathematics and physics, it is not surprising that various attempts have been made to define and study spectra also for nonlinear operators. This book provides a comprehensive and self-contained treatment of the theory, methods, and applications of nonlinear spectral theory. The first chapter briefly recalls the definition and properties of the spectrum and several subspectra for bounded linear operators. Then some numerical characteristics for nonlinear operators are introduced which are useful for describing those classes of operators for which there exists a spectral theory. Since spectral values are closely related to solvability results for operator equations, various conditions for the local or global invertibility of a nonlinear operator are collected in the third chapter. The following two chapters are concerned with spectra for certain classes of continuous, Lipschitz continuous, or differentiable operators. These spectra, however, simply adapt the corresponding definitions from the linear theory which somehow restricts their applicability. Other spectra which are defined in a completely different way, but seem to have useful applications, are defined and studied in the following four chapters. The remaining three chapters are more application-oriented and deal with nonlinear eigenvalue problems, numerical ranges, and selected applications to nonlinear problems. The only prerequisite for understanding this book is a modest background in functional analysis and operator theory. It is addressed to non-specialists who want to get an idea of the development of spectral theory for nonlinear operators in the last 30 years, as well as a glimpse of the diversity of the directions in which current research is moving.
Protecting Inventions In Chemistry
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Author : Bernd Hansen
language : en
Publisher: John Wiley & Sons
Release Date : 2008-07-11
Protecting Inventions In Chemistry written by Bernd Hansen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-11 with Law categories.
This book covers the protection of chemical inventions by means of Patents and Utility Models, as well as Supplementary Protection Certificates (SPCs) for medicaments and agrochemicals. The jurisdiction of both the European Patent Office and the relevant German Courts which has been developed in recent decades is presented and explained in a comparative manner. It is the first English edition of a book which has become a standard companion for Patent Practitioners in the field of Chemistry in German speaking countries. The material prerequisites of patentability such as novelty, inventive step and sufficiency are comprehensively discussed. Further included is an overview on the examination proceeding before both the European and German Patent Offices. Special emphasis has been given to Chapters VII-IX, dealing with the issues of protective scope, infringement proceeding (national and crossborder) and the exhaustion of patent rights. The latest Case Law of the Appeal Boards of the European Patent Office, the German Federal Supreme Court and the Federal Patent Court has been taken into account. This book provides all the information necessary for the acquisition, the use and the enforcement of protective rights in the field of chemistry. The authors of the commentary are Dr. Bernd Hansen, a Munich-based Patent Attorney and Dr. Fritjoff Hirsch, a former Judge of the German Federal Patent Court.