This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces.

Author: William Arveson

Publisher: Springer Science & Business Media

ISBN: 9780387215181

Category: Mathematics

Page: 142

View: 245

This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra: the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C*-algebras being three areas of current research activity which require mastery of the material presented here.

This succinct and enlightening overview is a required reading for all those interested in the subject . We hope you find this book useful in shaping your future career & Business.

Author: Ewan N. Singh

Publisher: CreateSpace

ISBN: 1517019257

Category:

Page: 80

View: 741

This updated and expanded second edition of the A Short Course on Spectral Theory (Graduate Texts in Mathematics) provides a user-friendly introduction to the subject, Taking a clear structural framework, it guides the reader through the subject's core elements. A flowing writing style combines with the use of illustrations and diagrams throughout the text to ensure the reader understands even the most complex of concepts. This succinct and enlightening overview is a required reading for all those interested in the subject . We hope you find this book useful in shaping your future career & Business. Feel free to send us your inquiries related to our publications to [email protected]

The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces.

Author: Klaus-Jochen Engel

Publisher: Springer Science & Business Media

ISBN: 9780387313412

Category: Mathematics

Page: 247

View: 443

The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. The book is intended for students and researchers who want to become acquainted with the concept of semigroups.

Y.A. Abramovich and C.D. Aliprantis, An Invitation to Operator Theory, Graduate Studies in Mathematics, Vol. 50, Amer. Math. Soc., Providence, 2002. 2. ... W. Arveson, A Short Course in Spectral Theory, Springer, New York, 2002. 8.

Author: Carlos S. Kubrusly

Publisher: Springer Nature

ISBN: 9783030331498

Category: Mathematics

Page: 249

View: 364

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.

[3] William Arveson, A short course on spectral theory, Graduate Texts in Mathematics, vol. 209, Springer-Verlag, New York, 2002. [4] S. Axler, J.B. Conway, and G. McDonald, Toeplitz operators on Bergman spaces, Canad. J. Math.

Author: Manuel Cepedello Boiso

Publisher: Springer Science & Business Media

ISBN: 9783034806480

Category: Mathematics

Page: 535

View: 627

This book contains a collection of research articles and surveys on recent developments on operator theory as well as its applications covered in the IWOTA 2011 conference held at Sevilla University in the summer of 2011. The topics include spectral theory, differential operators, integral operators, composition operators, Toeplitz operators, and more. The book also presents a large number of techniques in operator theory.

Spectral Theory Course Book is one of the series of books covering various topics of science, technology and management published by London School of Management Studies.

Author: Aidan N. Wood

Publisher: CreateSpace

ISBN: 1507795785

Category: Science

Page: 80

View: 581

Spectral Theory Course Book is one of the series of books covering various topics of science, technology and management published by London School of Management Studies. The book will cover the introduction to the Topic and can be used as a very useful course study material for students pursuing their studies in undergraduate and graduate levels in universities and colleges and those who want to learn the topic in brief via a short and complete resource. We hope you find this book useful is shaping your future career, Please send us your enquiries related to our publications to [email protected] London School of Management Studies www.lsms.org.uk

N.I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space, 2nd ed., Dover Publications, Inc., New York, 1993. W. Arveson, A Short Course in Spectral Theory, Graduate Texts in Mathematics, vol.209, Springer-Verlag, ...

Author: Marat V. Markin

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110600988

Category: Mathematics

Page: 425

View: 571

The book is intended as a text for a one-semester graduate course in operator theory to be taught "from scratch'', not as a sequel to a functional analysis course, with the basics of the spectral theory of linear operators taking the center stage. The book consists of six chapters and appendix, with the material flowing from the fundamentals of abstract spaces (metric, vector, normed vector, and inner product), the Banach Fixed-Point Theorem and its applications, such as Picard's Existence and Uniqueness Theorem, through the basics of linear operators, two of the three fundamental principles (the Uniform Boundedness Principle and the Open Mapping Theorem and its equivalents: the Inverse Mapping and Closed Graph Theorems), to the elements of the spectral theory, including Gelfand's Spectral Radius Theorem and the Spectral Theorem for Compact Self-Adjoint Operators, and its applications, such as the celebrated Lyapunov Stability Theorem. Conceived as a text to be used in a classroom, the book constantly calls for the student's actively mastering the knowledge of the subject matter. There are problems at the end of each chapter, starting with Chapter 2 and totaling at 150. Many important statements are given as problems and frequently referred to in the main body. There are also 432 Exercises throughout the text, including Chapter 1 and the Appendix, which require of the student to prove or verify a statement or an example, fill in certain details in a proof, or provide an intermediate step or a counterexample. They are also an inherent part of the material. More difficult problems are marked with an asterisk, many problems and exercises are supplied with "existential'' hints. The book is generous on Examples and contains numerous Remarks accompanying definitions, examples, and statements to discuss certain subtleties, raise questions on whether the converse assertions are true, whenever appropriate, or whether the conditions are essential. With carefully chosen material, proper attention given to applications, and plenty of examples, problems, and exercises, this well-designed text is ideal for a one-semester Master's level graduate course in operator theory with emphasis on spectral theory for students majoring in mathematics, physics, computer science, and engineering. Contents Preface Preliminaries Metric Spaces Vector Spaces, Normed Vector Spaces, and Banach Spaces Linear Operators Elements of Spectral Theory in a Banach Space Setting Elements of Spectral Theory in a Hilbert Space Setting Appendix: The Axiom of Choice and Equivalents Bibliography Index

Freiberger/Grenander: A Short Course in Computational Probability and Statistics. . Pipkin: Lectures on Viscoelasticity Theory. . Giacoglia: Perturbation Methods in Non-linear Systems. . Friedrichs: Spectral Theory of Operators in ...

Author: P.D. Hislop

Publisher: Springer Science & Business Media

ISBN: 9781461207412

Category: Mathematics

Page: 338

View: 533

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 Dijferential Operators, Cambridge Studies in Advanced Mathematics, Vol. 42. ... Pseudospectra, the harmonic oscillator and complex resonances. Proc. R. Soc. Lond. ... A Short Course on Operator Semi-Groups, Unitext.

Author: Bernard Helffer

Publisher: Cambridge University Press

ISBN: 9781107032309

Category: Mathematics

Page: 255

View: 224

Introduces the basic tools in spectral analysis using numerous examples from the Schrödinger operator theory and various branches of physics.

[Str05a] [Str05b] [Str11] [Var07] [Vla81] [Wald94] [War75] [Wei99] [Wes78] [Wig59] [Wigh95] [ZFC05] [Zeh00] Strocchi F.: An Introduction To The Mathematical Structure Of Quantum Mechanics: A Short Course For Mathematicians.

Author: Valter Moretti

Publisher: Springer Science & Business Media

ISBN: 9788847028357

Category: Mathematics

Page: 728

View: 169

This book pursues the accurate study of the mathematical foundations of Quantum Theories. It may be considered an introductory text on linear functional analysis with a focus on Hilbert spaces. Specific attention is given to spectral theory features that are relevant in physics. Having left the physical phenomenology in the background, it is the formal and logical aspects of the theory that are privileged. Another not lesser purpose is to collect in one place a number of useful rigorous statements on the mathematical structure of Quantum Mechanics, including some elementary, yet fundamental, results on the Algebraic Formulation of Quantum Theories. In the attempt to reach out to Master's or PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book should benefit established researchers to organise and present the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly.

Conference in Honor of James Ralston's 70th Birthday on Spectral Theory and Partial Differential Equations: June 17--21, 2013, ... MR1029119 (91a:35166) J. Lehner, A short course in automorphic functions, Holt, Rinehart and Winston, ...

Author: James V Ralston

Publisher: American Mathematical Soc.

ISBN: 9781470409890

Category: Differential equations, Partial

Page: 197

View: 396

This volume contains the proceedings of the Conference on Spectral Theory and Partial Differential Equations, held from June 17-21, 2013, at the University of California, Los Angeles, California, in honor of James Ralston's 70th Birthday. Papers in this volume cover important topics in spectral theory and partial differential equations such as inverse problems, both analytical and algebraic; minimal partitions and Pleijel's Theorem; spectral theory for a model in Quantum Field Theory; and beams on Zoll manifolds.

The first chapter deals with spectral theorem for operators in the finite dimensional case . The topic is developed keeping in mind two goals : ( i ) the treatment must be as geometric as possible , and ( ii ) it should be indicative of ...

Author: S. Kumaresan

Publisher: Universities Press

ISBN: 8173714533

Category: Mathematical analysis

Page: 151

View: 753

This book is a collection of lectures delivered by the author at mathematics instrutional workshop and refresher courses. Topics covered include the spectral theorem for operators in the finite dimensional case, Lebesgue integration theory via the Daniell method, Fourier transform on R, solution of the Dirichlet problem for the potential equation in the plane by Perron's method...

Aguilar/Gitler/Prieto: Algebraic Topology from a Homotopical Viewpoint Aksoy/Khamsi: Nonstandard Methods in Fixed Point Theory Andersson: Topics in Complex Analysis Aupetit: A Primer on Spectral Theory Bachman/Narici/Beckenstein: ...

Author: Klaus-Jochen Engel

Publisher: Springer Science & Business Media

ISBN: 9780387366197

Category: Mathematics

Page: 248

View: 449

The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. It contains the fundamental results of the theory such as the Hille-Yoshida generation theorem, the bounded perturbation theorem, and the Trotter-Kato approximation theorem. It also treats the spectral theory of semigroups and its consequences for the qualitative behavior. The book is intended for students and researchers who want to become acquainted with the concept of semigroups in order to work with it in fields like partial and functional differential equations. Exercises are provided at the end of the chapters.

D. Amir, Characterizations of Inner Product Spaces, Operator Theory: Advances and Applications, Vol. 20, Birkhäuser, Basel, 1986. 2. W. Arveson, A Short Course on Spectral Theory, Springer-Verlag, New York, 2002. 3.

Author: Barbara MacCluer

Publisher: Springer Science & Business Media

ISBN: 9780387855295

Category: Mathematics

Page: 208

View: 172

Functional analysis arose in the early twentieth century and gradually, conquering one stronghold after another, became a nearly universal mathematical doctrine, not merely a new area of mathematics, but a new mathematical world view. Its appearance was the inevitable consequence of the evolution of all of nineteenth-century mathematics, in particular classical analysis and mathematical physics. Its original basis was formed by Cantor’s theory of sets and linear algebra. Its existence answered the question of how to state general principles of a broadly interpreted analysis in a way suitable for the most diverse situations. A.M. Vershik ([45], p. 438). This text evolved from the content of a one semester introductory course in fu- tional analysis that I have taught a number of times since 1996 at the University of Virginia. My students have included ?rst and second year graduate students prep- ing for thesis work in analysis, algebra, or topology, graduate students in various departments in the School of Engineering and Applied Science, and several und- graduate mathematics or physics majors. After a ?rst draft of the manuscript was completed, it was also used for an independent reading course for several und- graduates preparing for graduate school.

Arveson, W. (2002) A Short Course on Spectral Theory (Springer). Atiyah, M. F. (1997) The index of elliptic operators, in Fields Medallists' Lectures, World Scientific and Singapore University Press, pp.115–127.

Author: M W Wong

Publisher: World Scientific Publishing Company

ISBN: 9789814583107

Category: Mathematics

Page: 196

View: 874

The aim of this third edition is to give an accessible and essentially self-contained account of pseudo-differential operators based on the previous edition. New chapters notwithstanding, the elementary and detailed style of earlier editions is maintained in order to appeal to the largest possible group of readers. The focus of this book is on the global theory of elliptic pseudo-differential operators on Lp(Rn). The main prerequisite for a complete understanding of the book is a basic course in functional analysis up to the level of compact operators. It is an ideal introduction for graduate students in mathematics and mathematicians who aspire to do research in pseudo-differential operators and related topics.

Rational Homotopy Theory. 2nd ed. MURTY. Problems in Analytic Number Theory. Readings in Mathematics GODSIL/ROYLE. Algebraic Graph Theory. CHENEY. Analysis for Applied Mathematics. ARVESON. A Short Course on Spectral Theory. ROSEN.

Author: Raymond O. Wells

Publisher: Springer Science & Business Media

ISBN: 9780387738918

Category: Mathematics

Page: 304

View: 683

A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Wells’s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. Oscar Garcia-Prada’s appendix gives an overview of the developments in the field during the decades since the book appeared.

Algebraic Graph Theory. CHENEY. Analysis for Applied Mathematics. ARVESON. A Short Course on Spectral Theory. ROSEN. Number Theory in Function Fields. LANG. Algebra. Revised 3rd ed. MATOUSEK. Lectures on Discrete Geometry.

Author: Henning Stichtenoth

Publisher: Springer Science & Business Media

ISBN: 9783540768784

Category: Mathematics

Page: 360

View: 905

This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.

A short course in spectral theory. New York: Springer-Verlag. 5. ... Spectra of composition operators with symbols in S.2/. Journal of Operator Theory, 75, 321–348. 8. Brown, J. W., & Churchill, R. V. (2009).

Author: Douglas Farenick

Publisher: Springer

ISBN: 9783319456331

Category: Mathematics

Page: 451

View: 224

This book provides a unique path for graduate or advanced undergraduate students to begin studying the rich subject of functional analysis with fewer prerequisites than is normally required. The text begins with a self-contained and highly efficient introduction to topology and measure theory, which focuses on the essential notions required for the study of functional analysis, and which are often buried within full-length overviews of the subjects. This is particularly useful for those in applied mathematics, engineering, or physics who need to have a firm grasp of functional analysis, but not necessarily some of the more abstruse aspects of topology and measure theory normally encountered. The reader is assumed to only have knowledge of basic real analysis, complex analysis, and algebra. The latter part of the text provides an outstanding treatment of Banach space theory and operator theory, covering topics not usually found together in other books on functional analysis. Written in a clear, concise manner, and equipped with a rich array of interesting and important exercises and examples, this book can be read for an independent study, used as a text for a two-semester course, or as a self-contained reference for the researcher.

A Short Course on Spectral Theory . 210 ROSEN . Number Theory in Function Fields . 211 LANG . Algebra . Revised 3rd ed . 212 MATOUŠEK . Lectures on Discrete Geometry 213 FRITZSCHE / GRAUERT . From Holomorphic Functions to Complex.

Author: David A Cox

Publisher: Springer Science & Business Media

ISBN: 0387207333

Category: Mathematics

Page: 12

View: 525

The discovery of new algorithms for dealing with polynomial equations, and their implementation on fast, inexpensive computers, has revolutionized algebraic geometry and led to exciting new applications in the field. This book details many uses of algebraic geometry and highlights recent applications of Grobner bases and resultants. This edition contains two new sections, a new chapter, updated references and many minor improvements throughout.