Numerical Range

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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 Range Of Holomorphic Mappings And Applications

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Author : Mark Elin
language : en
Publisher: Springer
Release Date : 2019-03-11

Numerical Range Of Holomorphic Mappings And Applications written by Mark Elin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-11 with Mathematics categories.

This book describes recent developments as well as some classical results regarding holomorphic mappings. The book starts with a brief survey of the theory of semigroups of linear operators including the Hille-Yosida and the Lumer-Phillips theorems. The numerical range and the spectrum of closed densely defined linear operators are then discussed in more detail and an overview of ergodic theory is presented. The analytic extension of semigroups of linear operators is also discussed. The recent study of the numerical range of composition operators on the unit disk is mentioned. Then, the basic notions and facts in infinite dimensional holomorphy and hyperbolic geometry in Banach and Hilbert spaces are presented, L. A. Harris' theory of the numerical range of holomorphic mappings is generalized, and the main properties of the so-called quasi-dissipative mappings and their growth estimates are studied. In addition, geometric and quantitative analytic aspects of fixed point theory are discussed. A special chapter is devoted to applications of the numerical range to diverse geometric and analytic problems.

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.

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 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.

Finding Ellipses What Blaschke Products Poncelet S Theorem And The Numerical Range Know About Each Other

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Author : Ulrich Daepp
language : en
Publisher: American Mathematical Soc.
Release Date : 2018

Finding Ellipses What Blaschke Products Poncelet S Theorem And The Numerical Range Know About Each Other written by Ulrich Daepp 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 2018 with Mathematics categories.

Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry.

A Hilbert Space Problem Book

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Author : P.R. Halmos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

A Hilbert Space Problem Book written by P.R. Halmos 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.

From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."

Matrix Theory A Second Course

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Author : James M. Ortega
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Matrix Theory A Second Course written by James M. Ortega 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 2013-11-11 with Mathematics categories.

Linear algebra and matrix theory are essentially synonymous terms for an area of mathematics that has become one of the most useful and pervasive tools in a wide range of disciplines. It is also a subject of great mathematical beauty. In consequence of both of these facts, linear algebra has increasingly been brought into lower levels of the curriculum, either in conjunction with the calculus or separate from it but at the same level. A large and still growing number of textbooks has been written to satisfy this need, aimed at students at the junior, sophomore, or even freshman levels. Thus, most students now obtaining a bachelor's degree in the sciences or engineering have had some exposure to linear algebra. But rarely, even when solid courses are taken at the junior or senior levels, do these students have an adequate working knowledge of the subject to be useful in graduate work or in research and development activities in government and industry. In particular, most elementary courses stop at the point of canonical forms, so that while the student may have "seen" the Jordan and other canonical forms, there is usually little appreciation of their usefulness. And there is almost never time in the elementary courses to deal with more specialized topics like nonnegative matrices, inertia theorems, and so on. In consequence, many graduate courses in mathematics, applied mathe matics, or applications develop certain parts of matrix theory as needed.

Glasnik Matematicki

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Author :
language : en
Publisher:
Release Date : 1983

Glasnik Matematicki written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.

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.