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A Hilbert Space Problem Book

A Hilbert Space Problem Book PDF Author: P.R. Halmos
Publisher: Springer Science & Business Media
ISBN: 1468493302
Category : Mathematics
Languages : en
Pages : 385

Book Description
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."

A Hilbert Space Problem Book

A Hilbert Space Problem Book PDF Author: P.R. Halmos
Publisher: Springer Science & Business Media
ISBN: 1468493302
Category : Mathematics
Languages : en
Pages : 385

Book Description
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."

Hilbert-Courant

Hilbert-Courant PDF Author: Constance Reid
Publisher: Springer Science & Business Media
ISBN: 9780387962566
Category : Biography & Autobiography
Languages : en
Pages : 620

Book Description
I am very pleased that my books about David Hilbert, published in 1970, and Richard Courant, published in 1976, are now being issued by Springer Verlag in a single volume. I have always felt that they belonged together, Courant being, as I have written, the natural and necessary sequel to Hilbert the rest of the story. To make the two volumes more compatible when published as one, we have combined and brought up to date the indexes of names and dates. U nfortu nately we have had to omit Hermann Weyl's article on "David Hilbert and his mathematical work," but the interested reader can always find it in the hard back edition of Hilbert and in Weyl's collected papers. At the request of a number of readers we have included a listing of all of Hilbert's famous Paris problems. It was, of course, inevitable that we would give the resulting joint volume the title Hilbert-Courant.

The Foundations of Geometry

The Foundations of Geometry PDF Author: David Hilbert
Publisher: Read Books Ltd
ISBN: 1473395941
Category : History
Languages : en
Pages : 139

Book Description
This early work by David Hilbert was originally published in the early 20th century and we are now republishing it with a brand new introductory biography. David Hilbert was born on the 23rd January 1862, in a Province of Prussia. Hilbert is recognised as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.

An Introduction to Hilbert Space and Quantum Logic

An Introduction to Hilbert Space and Quantum Logic PDF Author: David W. Cohen
Publisher: Springer Science & Business Media
ISBN: 1461388414
Category : Science
Languages : en
Pages : 159

Book Description
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.

Applied Analysis by the Hilbert Space Method

Applied Analysis by the Hilbert Space Method PDF Author: Samuel S. Holland
Publisher: Courier Corporation
ISBN: 0486139298
Category : Mathematics
Languages : en
Pages : 578

Book Description
Numerous worked examples and exercises highlight this unified treatment. Simple explanations of difficult subjects make it accessible to undergraduates as well as an ideal self-study guide. 1990 edition.

Hilbert's Fifth Problem and Related Topics

Hilbert's Fifth Problem and Related Topics PDF Author: Terence Tao
Publisher: American Mathematical Soc.
ISBN: 147041564X
Category : Mathematics
Languages : en
Pages : 354

Book Description
In the fifth of his famous list of 23 problems, Hilbert asked if every topological group which was locally Euclidean was in fact a Lie group. Through the work of Gleason, Montgomery-Zippin, Yamabe, and others, this question was solved affirmatively; more generally, a satisfactory description of the (mesoscopic) structure of locally compact groups was established. Subsequently, this structure theory was used to prove Gromov's theorem on groups of polynomial growth, and more recently in the work of Hrushovski, Breuillard, Green, and the author on the structure of approximate groups. In this graduate text, all of this material is presented in a unified manner, starting with the analytic structural theory of real Lie groups and Lie algebras (emphasising the role of one-parameter groups and the Baker-Campbell-Hausdorff formula), then presenting a proof of the Gleason-Yamabe structure theorem for locally compact groups (emphasising the role of Gleason metrics), from which the solution to Hilbert's fifth problem follows as a corollary. After reviewing some model-theoretic preliminaries (most notably the theory of ultraproducts), the combinatorial applications of the Gleason-Yamabe theorem to approximate groups and groups of polynomial growth are then given. A large number of relevant exercises and other supplementary material are also provided.

Hilbert's Programs and Beyond

Hilbert's Programs and Beyond PDF Author: Wilfried Sieg
Publisher: Oxford University Press
ISBN: 0195372220
Category : Computers
Languages : en
Pages : 452

Book Description
David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations.

An Introduction to Hilbert Space

An Introduction to Hilbert Space PDF Author: N. Young
Publisher: Cambridge University Press
ISBN: 1107717167
Category : Mathematics
Languages : en
Pages : 254

Book Description
This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to 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. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it 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.

Hilbert Space Methods in Probability and Statistical Inference

Hilbert Space Methods in Probability and Statistical Inference PDF Author: Christopher G. Small
Publisher: John Wiley & Sons
ISBN: 1118165535
Category : Mathematics
Languages : en
Pages : 268

Book Description
Explains how Hilbert space techniques cross the boundaries into the foundations of probability and statistics. Focuses on the theory of martingales stochastic integration, interpolation and density estimation. Includes a copious amount of problems and examples.

From Kant to Hilbert Volume 1

From Kant to Hilbert Volume 1 PDF Author: William Bragg Ewald
Publisher: Oxford University Press, USA
ISBN: 0198505353
Category : Mathematics
Languages : en
Pages : 695

Book Description
This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics - algebra, geometry, number theory, analysis, logic, and set theory - with narratives to show how they are linked.