Spectral Theory of Bounded Linear Operators

Spectral Theory of Bounded Linear Operators PDF

Author: Carlos S. Kubrusly

Publisher: Springer Nature

Published: 2020-01-30

Total Pages: 249

ISBN-13: 3030331490

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This textbook introduces spectral theory for bounded linear operators by focusing on (i) the spectral theory and functional calculus for normal operators acting on Hilbert spaces; (ii) the Riesz-Dunford functional calculus for Banach-space operators; and (iii) the Fredholm theory in both Banach and Hilbert spaces. Detailed proofs of all theorems are included and presented with precision and clarity, especially for the spectral theorems, allowing students to thoroughly familiarize themselves with all the important concepts. Covering both basic and more advanced material, the five chapters and two appendices of this volume provide a modern treatment on spectral theory. Topics range from spectral results on the Banach algebra of bounded linear operators acting on Banach spaces to functional calculus for Hilbert and Banach-space operators, including Fredholm and multiplicity theories. Supplementary propositions and further notes are included as well, ensuring a wide range of topics in spectral theory are covered. Spectral Theory of Bounded Linear Operators is ideal for graduate students in mathematics, and will also appeal to a wider audience of statisticians, engineers, and physicists. Though it is mostly self-contained, a familiarity with functional analysis, especially operator theory, will be helpful.

Spectral Theory and Differential Operators

Spectral Theory and Differential Operators PDF

Author: David Eric Edmunds

Publisher: Oxford University Press

Published: 2018

Total Pages: 610

ISBN-13: 0198812051

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This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.--

Introduction to Spectral Theory in Hilbert Space

Introduction to Spectral Theory in Hilbert Space PDF

Author: Gilbert Helmberg

Publisher: Elsevier

Published: 2014-11-28

Total Pages: 362

ISBN-13: 1483164179

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North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of linear operators and spectral analysis of compact linear operators, including spectral decomposition of a compact selfadjoint operator, weakly convergent sequences, spectrum of a compact linear operator, and eigenvalues of a linear operator. The manuscript ponders on the spectral analysis of bounded linear operators and unbounded selfadjoint operators. Topics include spectral decomposition of an unbounded selfadjoint operator and bounded normal operator, functions of a unitary operator, step functions of a bounded selfadjoint operator, polynomials in a bounded operator, and order relation for bounded selfadjoint operators. The publication is a valuable source of data for mathematicians and researchers interested in spectral theory in Hilbert space.

Introduction to Spectral Theory

Introduction to Spectral Theory PDF

Author: P.D. Hislop

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 331

ISBN-13: 146120741X

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The intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.

Spectral Theory and Differential Operators

Spectral Theory and Differential Operators PDF

Author: David Edmunds

Publisher: Oxford University Press

Published: 2018-05-03

Total Pages:

ISBN-13: 0192540106

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This book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators".The original book was a cutting edge account of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.

Spectral Theory of Operators on Hilbert Spaces

Spectral Theory of Operators on Hilbert Spaces PDF

Author: Carlos S. Kubrusly

Publisher: Springer Science & Business Media

Published: 2012-06-01

Total Pages: 203

ISBN-13: 0817683283

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This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreated. Spectral Theory of Operators on Hilbert Spaces is addressed to an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. It will also be useful to working mathematicians using spectral theory of Hilbert space operators, as well as for scientists wishing to apply spectral theory to their field. ​

Spectral Theory and Differential Operators

Spectral Theory and Differential Operators PDF

Author: E. Brian Davies

Publisher: Cambridge University Press

Published: 1995

Total Pages: 198

ISBN-13: 9780521587105

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This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on partial differential operators.

Spectral Theory on the S-Spectrum for Quaternionic Operators

Spectral Theory on the S-Spectrum for Quaternionic Operators PDF

Author: Fabrizio Colombo

Publisher: Springer

Published: 2019-01-04

Total Pages: 356

ISBN-13: 3030030741

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The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum. With the purpose of giving a systematic and self-contained treatment of this theory that has been developed in the last decade, the book features topics like the S-functional calculus, the F-functional calculus, the quaternionic spectral theorem, spectral integration and spectral operators in the quaternionic setting. These topics are based on the notion of S-spectrum of a quaternionic linear operator. Further developments of this theory lead to applications in fractional diffusion and evolution problems that will be covered in a separate monograph.

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