A Hilbert Space Problem Book

Author: P.R. Halmos
Publisher: Springer Science & Business Media
ISBN: 9781461599760
Release Date: 2012-12-06
Genre: Mathematics

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: 3525405278
Release Date: 1976
Genre: Arithmetic


An Introduction to Hilbert Space

Author: N. Young
Publisher: Cambridge University Press
ISBN: 0521337178
Release Date: 1988-07-21
Genre: Mathematics

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.

An Advanced Complex Analysis Problem Book

Author: Daniel Alpay
Publisher: Birkhäuser
ISBN: 9783319160597
Release Date: 2015-11-13
Genre: Mathematics

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 Hilbertr umen

Author: Joachim Weidmann
Publisher: Springer-Verlag
ISBN: 3322800946
Release Date: 2013-03-08
Genre: Mathematics

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

Theory of Bergman Spaces

Author: Hakan Hedenmalm
Publisher: Springer Science & Business Media
ISBN: 9781461204978
Release Date: 2012-12-06
Genre: Mathematics

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.

Unbounded Self adjoint Operators on Hilbert Space

Author: Konrad Schmüdgen
Publisher: Springer Science & Business Media
ISBN: 9789400747531
Release Date: 2012-07-09
Genre: Mathematics

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

Hilbert Space Methods in Partial Differential Equations

Author: Ralph E. Showalter
Publisher: Courier Corporation
ISBN: 9780486135793
Release Date: 2011-09-12
Genre: Mathematics

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.

Finite Dimensional Vector Spaces AM 7

Author: Paul R. Halmos
Publisher: Princeton University Press
ISBN: 9781400882236
Release Date: 2016-03-02
Genre: Mathematics

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."

A Primer on Hilbert Space Theory

Author: Carlo Alabiso
Publisher: Springer
ISBN: 9783319037134
Release Date: 2014-10-08
Genre: Science

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.

An Introduction to Hilbert Space and Quantum Logic

Author: David W. Cohen
Publisher: Springer Science & Business Media
ISBN: 9781461388418
Release Date: 2012-12-06
Genre: Science

Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence each other we hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed.

Hilbert Spaces of Analytic Functions

Author: Javad Mashreghi
Publisher: American Mathematical Soc.
ISBN: 9780821870457
Release Date: 2010-01-01
Genre: Mathematics

Hilbert spaces of analytic functions are currently a very active field of complex analysis. The Hardy space is the most senior member of this family. However, other classes of analytic functions such as the classical Bergman space, the Dirichlet space, the de Branges-Rovnyak spaces, and various spaces of entire functions, have been extensively studied. These spaces have been exploited in different fields of mathematics and also in physics and engineering. For example, de Branges used them to solve the Bieberbach conjecture. Modern control theory is another place that heavily exploits the techniques of analytic function theory. This book grew out of a workshop held in December 2008 at the CRM in Montreal and provides an account of the latest developments in the field of analytic function theory. Titles in this series are co-published with the Centre de Recherches Mathematiques. (CRMP/51)

Advanced Linear Algebra

Author: Steven Roman
Publisher: Springer Science & Business Media
ISBN: 9780387728315
Release Date: 2007-09-20
Genre: Mathematics

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.