A Hilbert Space Problem Book


Author: P.R. Halmos

Publisher: Springer Science & Business Media

ISBN: 1461599768

Category: Mathematics

Page: 365

View: 2126

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."

Naive Mengenlehre


Author: Paul R. Halmos

Publisher: Vandenhoeck & Ruprecht

ISBN: 9783525405277

Category: Arithmetic

Page: 132

View: 8015

An Advanced Complex Analysis Problem Book

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


Author: Daniel Alpay

Publisher: Birkhäuser

ISBN: 3319160591

Category: Mathematics

Page: 521

View: 4802

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.

Lineare Operatoren in Hilberträumen

Teil 1 Grundlagen


Author: Joachim Weidmann

Publisher: Springer-Verlag

ISBN: 9783322800947

Category: Mathematics

Page: 475

View: 3756

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

An Introduction to Hilbert Space


Author: N. Young

Publisher: Cambridge University Press

ISBN: 9780521337175

Category: Mathematics

Page: 239

View: 9683

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.

Real and Abstract Analysis

A modern treatment of the theory of functions of a real variable


Author: Edwin Hewitt,Karl Stromberg

Publisher: Springer-Verlag

ISBN: 3662297949

Category: Mathematics

Page: 476

View: 6756

Theory of Bergman Spaces


Author: Hakan Hedenmalm,Boris Korenblum,Kehe Zhu

Publisher: Springer Science & Business Media

ISBN: 1461204976

Category: Mathematics

Page: 289

View: 1552

Fifteen years ago, most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely, yet today the situation has completely changed. For several years, research interest and activity have expanded in this area and there are now rich theories describing the Bergman spaces and their operators. This book is a timely treatment of the theory, written by three of the major players in the field.

Lineare Funktionalanalysis

Eine anwendungsorientierte Einführung


Author: Hans Wilhelm Alt

Publisher: Springer-Verlag

ISBN: 3662083868

Category: Mathematics

Page: 294

View: 9245

Methoden der Mathematischen Physik


Author: Richard Courant,David Hilbert

Publisher: Springer-Verlag

ISBN: 3642474349

Category: Mathematics

Page: N.A

View: 4121

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

A Primer on Hilbert Space Theory

Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups


Author: Carlo Alabiso,Ittay Weiss

Publisher: Springer

ISBN: 3319037137

Category: Science

Page: 255

View: 719

This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all subjects has been enriched. Moreover, a brief introduction to topological groups has been added in addition to exercises and solved problems throughout the text. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.


Die seltsame Theorie des Lichts und der Materie


Author: Richard P. Feynman

Publisher: Piper Verlag

ISBN: 3492959865

Category: Science

Page: 176

View: 9256

Richard P. Feynman (1918–1988) erhielt 1965 für seine Beiträge zur Quantenelektrodynamik (QED) den Nobelpreis für Physik. Seine spektakulären Arbeiten zur »Theorie des Lichts und der Materie« erklärt der »brillanteste, respektloseste und einflussreichste theoretische Physiker der Nachkriegszeit« (The New York Times) hier auch für Nichtphysiker.

Unbounded Self-adjoint Operators on Hilbert Space


Author: Konrad Schmüdgen

Publisher: Springer Science & Business Media

ISBN: 9400747535

Category: Mathematics

Page: 432

View: 2054

The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises. The main themes of the book are the following: - Spectral integrals and spectral decompositions of self-adjoint and normal operators - Perturbations of self-adjointness and of spectra of self-adjoint operators - Forms and operators - Self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extension

Advanced Linear Algebra


Author: Steven Roman

Publisher: Springer Science & Business Media

ISBN: 0387728317

Category: Mathematics

Page: 525

View: 7874

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.

Functional analysis


Author: Harro Heuser

Publisher: John Wiley & Sons


Category: Mathematics

Page: 408

View: 4939

Finite Dimensional Vector Spaces. (AM-7)


Author: Paul R. Halmos

Publisher: Princeton University Press

ISBN: 1400882230

Category: Mathematics

Page: 196

View: 5945

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."

Mathematische Edelsteine

der elementaren Kombinatorik, Zahlentheorie und Geometrie


Author: Ross Honsberger

Publisher: Springer-Verlag

ISBN: 3322859304

Category: Mathematics

Page: 179

View: 9675

Hilbert Space Methods in Partial Differential Equations


Author: Ralph E. Showalter

Publisher: Courier Corporation

ISBN: 0486135799

Category: Mathematics

Page: 224

View: 4850

This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.

Lineare Algebra


Author: Werner Greub

Publisher: Springer-Verlag

ISBN: 3642663850

Category: Mathematics

Page: 222

View: 1358