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An Introduction To Hilbert Space

Author : N. Young
ISBN : 0521337178
Genre : Mathematics
File Size : 37. 68 MB
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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.

A Hilbert Space Problem Book

Author : P.R. Halmos
ISBN : 9781461599760
Genre : Mathematics
File Size : 43. 26 MB
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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."


Author : Constance Reid
ISBN : 9781461207399
Genre : Language Arts & Disciplines
File Size : 70. 34 MB
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"It presents a sensitive portrait of a great human being. It describes accurately and intelligibly on a nontechnical level the world of mathematical ideas in which Hilbert created his masterpieces. And it illuminates the background of German social history against which the drama of Hilberts life was played. Beyond this, it is a poem in praise of mathematics." -SCIENCE

Hilbert Courant

Author : Constance Reid
ISBN : 0387962565
Genre : Biography & Autobiography
File Size : 56. 67 MB
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David Hilbert, Director of the Mathematical Institute of G”ttingen during its glory years, is the formulator of the famous Hilbert Problems that set the course of mathematics from 1900 until the present day. In his prime, Hilbert was rivaled in influence only by the great Henri Poincare in Paris. Richard Courant was Hilbert's student and successor as director of the Mathematical Institute until his forcible removal in 1933. He co-authored Methods of Mathematical Physics (1924) with Hilbert, a classic text that seemed almost clairvoyant in its prediction of the mathematical needs of quantum physics. He also founded the Courant Institute at New York University. Poignant, lively and fascinating, these two books present a sweeping history of twentieth-century mathematics as it was expressed through the lives of these two great friends and colleagues. Constance Reid has been called 'the foremost mathematical biographer of our time.' Her many books include From Zero to Infinity, AELong Way from Euclid, The Search for E.T. Bell, and Neyman, from Life.

Geometry And The Imagination

Author : David Hilbert
ISBN : 9780821819982
Genre : Mathematics
File Size : 77. 67 MB
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This remarkable book endures as a true masterpiece of mathematical exposition. The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians. Geometry and the Imagination is full of interesting facts, many of which you wish you had known before. The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in $\mathbb{R}^3$. In this chapter, they also discuss plane lattices. By considering unit lattices, and throwing in a small amount of number theory when necessary, they effortlessly derive Leibniz's series: $\pi/4 = 1 - 1/3 + 1/5 - 1/7 + - \ldots$. In the section on lattices in three and more dimensions, the authors consider sphere-packing problems, including the famous Kepler problem. One of the most remarkable chapters is ``Projective Configurations''. In a short introductory section, Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. The chapter on kinematics includes a nice discussion of linkages and the geometry of configurations of points and rods that are connected and, perhaps, constrained in some way. This topic in geometry has become increasingly important in recent times, especially in applications to robotics. This is another example of a simple situation that leads to a rich geometry. It would be hard to overestimate the continuing influence Hilbert-Cohn-Vossen's book has had on mathematicians of this century. It surely belongs in the "pantheon" of great mathematics books.

Harmonic Analysis On Hilbert Spaces

Author : Leonard Gross
ISBN : STANFORD:36105002008071
Genre : Mathematics
File Size : 67. 17 MB
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Hilbert Space

Author : J. R. Retherford
ISBN : 0521429331
Genre : Mathematics
File Size : 76. 52 MB
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The aim of this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory leading to an elementary proof of the Lidskij trace theorem. The author assumes the reader is familiar with linear algebra and advanced calculus, and develops everything needed to introduce the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators. Many exercises and hints are included, and throughout the emphasis is on a user-friendly approach.

Hilbert Modules Over Operator Algebras

Author : Paul S. Muhly
ISBN : 9780821803462
Genre : Mathematics
File Size : 34. 98 MB
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This book gives a general systematic analysis of the notions of ``projectivity'' and ``injectivity'' in the context of Hilbert modules over operator algebras. A Hilbert module over an operator algebra $A$ is simply the Hilbert space of a (contractive) representation of $A$ viewed as a module over $A$ in the usual way. In this work, Muhly and Solel introduce various notions of projective Hilbert modules and use them to investigate dilation and commutant lifting problems over certain infinite dimensional analogues of incidence algebras. The authors prove that commutant lifting holds for such an algebra if and only if the pattern indexing the algebra is a ``tree'' in the sense of computer directories.

Fake Topological Hilbert Spaces And Characterizations Of Dimension In Terms Of Negligibility

Author : J. J. Dijkstra
ISBN : 9061962684
Genre : Mathematics
File Size : 47. 69 MB
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Hilbert C Modules

Author : E. Christopher Lance
ISBN : 052147910X
Genre : Mathematics
File Size : 62. 62 MB
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The theory of these modules together with their bounded and unbounded operators is not only rich and attractive in its own right but forms an infrastructure for some of the most important research topics in operator algebra. This book provides a clear and unified exposition of the main techniques and results in this area, including a substantial amount of new and unpublished material. Graduate students and researchers working in operator algebras will welcome this book as an excellent resource.

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