A Hilbert Space Problem Book

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Author: P.R. Halmos

Publisher: Springer Science & Business Media

ISBN: 1461599768

Category: Mathematics

Page: 365

View: 3898

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."

Lineare Operatoren in Hilberträumen

Teil 1 Grundlagen

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Author: Joachim Weidmann

Publisher: Springer-Verlag

ISBN: 9783322800947

Category: Mathematics

Page: 475

View: 2413

Behandelt werden die Grundlagen der Theorie zum Thema Lineare Operatoren in Hilberträumen, wie sie üblicherweise in Standardvorlesungen für Mathematiker und Physiker vorgestellt werden.

An Advanced Complex Analysis Problem Book

Topological Vector Spaces, Functional Analysis, and Hilbert Spaces of Analytic Functions

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Author: Daniel Alpay

Publisher: Birkhäuser

ISBN: 3319160591

Category: Mathematics

Page: 521

View: 6155

This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.

An Introduction to Hilbert Space

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Author: N. Young

Publisher: Cambridge University Press

ISBN: 9780521337175

Category: Mathematics

Page: 239

View: 9124

This textbook is an introduction to the theory of Hilbert spaces and its applications. The notion of a Hilbert space is a central idea in functional analysis and can be used in numerous branches of pure and applied mathematics. Dr. Young stresses these applications particularly for the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. The book is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). The book will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.

Lineare Operatoren in Hilberträumen

Teil II: Anwendungen

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Author: Joachim Weidmann

Publisher: Springer-Verlag

ISBN: 3322800954

Category: Mathematics

Page: 404

View: 1144

Die im ersten Teil des Buchs dargestellten Grundlagen der Theorie der linearen Operatoren in Hilberträumen werden hier benutzt, um die Spektraltheorie von Ein- und Mehrteilchen-Schrödingeroperatoren sowie des Dirac-Operators eingehend zu untersuchen.

A Short Course on Spectral Theory

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Author: William Arveson

Publisher: Springer Science & Business Media

ISBN: 0387215182

Category: Mathematics

Page: 142

View: 6064

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.

Finite Dimensional Vector Spaces. (AM-7)

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Author: Paul R. Halmos

Publisher: Princeton University Press

ISBN: 1400882230

Category: Mathematics

Page: 196

View: 9520

As a newly minted Ph.D., Paul Halmos came to the Institute for Advanced Study in 1938--even though he did not have a fellowship--to study among the many giants of mathematics who had recently joined the faculty. He eventually became John von Neumann's research assistant, and it was one of von Neumann's inspiring lectures that spurred Halmos to write Finite Dimensional Vector Spaces. The book brought him instant fame as an expositor of mathematics. Finite Dimensional Vector Spaces combines algebra and geometry to discuss the three-dimensional area where vectors can be plotted. The book broke ground as the first formal introduction to linear algebra, a branch of modern mathematics that studies vectors and vector spaces. The book continues to exert its influence sixty years after publication, as linear algebra is now widely used, not only in mathematics but also in the natural and social sciences, for studying such subjects as weather problems, traffic flow, electronic circuits, and population genetics. In 1983 Halmos received the coveted Steele Prize for exposition from the American Mathematical Society for "his many graduate texts in mathematics dealing with finite dimensional vector spaces, measure theory, ergodic theory, and Hilbert space."

Algebraic Topology

A First Course

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Author: William Fulton

Publisher: Springer Science & Business Media

ISBN: 1461241804

Category: Mathematics

Page: 430

View: 6810

To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind ing numbers and degrees of mappings, fixed-point theorems; appli cations such as the Jordan curve theorem, invariance of domain; in dices of vector fields and Euler characteristics; fundamental groups

Functional analysis

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Author: Harro Heuser

Publisher: John Wiley & Sons

ISBN: N.A

Category: Mathematics

Page: 408

View: 766

Matrix Analysis

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Author: Rajendra Bhatia

Publisher: Springer Science & Business Media

ISBN: 1461206537

Category: Mathematics

Page: 349

View: 3412

This book presents a substantial part of matrix analysis that is functional analytic in spirit. Topics covered include the theory of majorization, variational principles for eigenvalues, operator monotone and convex functions, and perturbation of matrix functions and matrix inequalities. The book offers several powerful methods and techniques of wide applicability, and it discusses connections with other areas of mathematics.

Deutsches Bücherverzeichnis

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: German literature

Page: N.A

View: 8127

Bde. 16, 18, 21, and 28 each contain section "Verlagsveränderüngen im deutschen Buchhandel."

Integration and Probability

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Author: Paul Malliavin

Publisher: Springer Science & Business Media

ISBN: 1461242029

Category: Mathematics

Page: 326

View: 5273

An introduction to analysis with the right mix of abstract theories and concrete problems. Starting with general measure theory, the book goes on to treat Borel and Radon measures and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the corresponding Fourier analysis. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's "stochastic calculus of variations" developed in the context of Gaussian measure spaces. This invaluable contribution gives a taste of the fact that analysis is not a collection of independent theories, but can be treated as a whole.

Field Theory

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Author: Steven Roman

Publisher: Springer Science & Business Media

ISBN: 0387276785

Category: Mathematics

Page: 335

View: 5896

"Springer has just released the second edition of Steven Roman’s Field Theory, and it continues to be one of the best graduate-level introductions to the subject out there....Every section of the book has a number of good exercises that would make this book excellent to use either as a textbook or to learn the material on your own. All in all...a well-written expository account of a very exciting area in mathematics." --THE MAA MATHEMATICAL SCIENCES DIGITAL LIBRARY

Advanced Real Analysis

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Author: Anthony W. Knapp

Publisher: Springer Science & Business Media

ISBN: 9780817644420

Category: Mathematics

Page: 466

View: 6573

* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician

Advanced Linear Algebra

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Author: Steven Roman

Publisher: Springer Science & Business Media

ISBN: 0387728317

Category: Mathematics

Page: 525

View: 2648

This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems.