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J-Contractive Matrix Valued Functions and Related Topics

J-Contractive Matrix Valued Functions and Related Topics
Author: Damir Z. Arov
Publisher: Cambridge University Press
Total Pages: 576
Release: 2008-11-06
Genre: Mathematics
ISBN: 0521883008

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A comprehensive introduction to the theory of J-contractive and J-inner matrix valued functions with respect to the open upper half-plane and a number of applications of this theory. It will be of particular interest to those with an interest in operator theory and matrix analysis.


$J$ Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation

$J$ Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation
Author: Harry Dym
Publisher: American Mathematical Soc.
Total Pages: 159
Release: 1989
Genre: Mathematics
ISBN: 0821807226

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Presents an introduction to the theory and applications of $J$ inner matrices. This book discusses matrix interpolation problems including two-sided tangential problems of both the Nevanlinna-Pick type and the Caratheodory-Fejer type, as well as mixtures of these.


Matrix and Operator Valued Functions

Matrix and Operator Valued Functions
Author: Israel Gohberg
Publisher: Birkhauser
Total Pages: 211
Release: 1994
Genre: Mathematics
ISBN: 9780817650919

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Non-Associative Normed Algebras: Volume 1, The Vidav–Palmer and Gelfand–Naimark Theorems

Non-Associative Normed Algebras: Volume 1, The Vidav–Palmer and Gelfand–Naimark Theorems
Author: Miguel Cabrera García
Publisher: Cambridge University Press
Total Pages: 735
Release: 2014-07-31
Genre: Mathematics
ISBN: 1139992775

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This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This first volume focuses on the non-associative generalizations of (associative) C*-algebras provided by the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems, which give rise to alternative C*-algebras and non-commutative JB*-algebras, respectively. The relationship between non-commutative JB*-algebras and JB*-triples is also fully discussed. The second volume covers Zel'manov's celebrated work in Jordan theory to derive classification theorems for non-commutative JB*-algebras and JB*-triples, as well as other topics. The book interweaves pure algebra, geometry of normed spaces, and complex analysis, and includes a wealth of historical comments, background material, examples and exercises. The authors also provide an extensive bibliography.


Stochastic Equations in Infinite Dimensions

Stochastic Equations in Infinite Dimensions
Author: Giuseppe Da Prato
Publisher: Cambridge University Press
Total Pages: 513
Release: 2014-04-17
Genre: Mathematics
ISBN: 1107055849

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Updates in this second edition include two brand new chapters and an even more comprehensive bibliography.


Non-Associative Normed Algebras

Non-Associative Normed Algebras
Author: Miguel Cabrera García
Publisher: Cambridge University Press
Total Pages: 735
Release: 2014-07-31
Genre: Mathematics
ISBN: 1107043069

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The first systematic account of the basic theory of normed algebras, without assuming associativity. Sure to become a central resource.


Orthogonal Polynomials of Several Variables

Orthogonal Polynomials of Several Variables
Author: Charles F. Dunkl
Publisher: Cambridge University Press
Total Pages: 439
Release: 2014-08-21
Genre: Mathematics
ISBN: 1107071895

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Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.


Convex Functions

Convex Functions
Author: Jonathan M. Borwein
Publisher: Cambridge University Press
Total Pages: 533
Release: 2010-01-14
Genre: Mathematics
ISBN: 1139811096

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Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level.


Convex Bodies: The Brunn–Minkowski Theory

Convex Bodies: The Brunn–Minkowski Theory
Author: Rolf Schneider
Publisher: Cambridge University Press
Total Pages: 759
Release: 2014
Genre: Mathematics
ISBN: 1107601010

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A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.


Ellipsoidal Harmonics

Ellipsoidal Harmonics
Author: George Dassios
Publisher: Cambridge University Press
Total Pages: 475
Release: 2012-07-12
Genre: Mathematics
ISBN: 1139510134

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The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal geometry and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally boundary value problems. End-of-chapter problems complement the theory and test the reader's understanding. The book serves as a comprehensive reference for applied mathematicians, physicists, engineers and for anyone who needs to know the current state of the art in this fascinating subject.