Bratteli, Ola; Neshveyev, Sergey; Skau, Christian (Eds.)

Operator Algebras
The Abel Symposium 2004

Series: Abel Symposia , Vol. 1
2006, Hardcover.
ISBN: 3-540-34196-X
Due: August 2, 2006

About this book

The theme of the first Abel Symposium was operator algebras in a wide sense. In the last 40 years operator algebras have developed from a rather special discipline within functional analysis to become a central field in mathematics often described as "non-commutative geometry". It has branched out in several sub-disciplines and made contact with other subjects. The contributions to this volume give a state-of-the-art account of some of these sub-disciplines and the variety of topics reflect to some extent how the subject has developed. This is the first volume in a prestigious new book series linked to the Abel prize.

Written for:

Researchers, graduate students in mathematics and mathematical physics

Table of contents

Lawrence G. Brown and Gert K. Pedersen: Interpolation by Projections in C*-Algebras.- Alain Connes, Matilde Marcolli and Niranjan Ramachandran: KMS states and complex multiplication (Part II).- Joachim Cuntz: An algebraic description of boundary maps used in index theory.- Soren Eilers and Gunnar Restorff: On Rordam's classification of certain C*-algebras with one non-trivial ideal.- George A. Elliott and Mikael Rordam: Perturbation of Hausdorff moment sequences, and an application to the theory of C*-algebras of real rank zero.- David E. Evans: Twisted K-theory and Modular Invariants: I Quantum Doubles of Finite Groups.- Thierry Giordano, Ian F. Putnam and Christian F. Skau: The Orbit Structure of Cantor Minimal Z2-Systems.- Yoshikazu Katayama and Masamichi Takesaki: Outer Actions of a Group on a Factor.- Takeshi Katsura: Non-separable AF-algebras.- Eberhard Kirchberg: Central sequences in C*-algebras and strongly purely infinite algebras.- Akitaka Kishimoto: Lifting of an asymptotically inner flow for a separable C*-algebra.- Dimitri Shlyakhtenko: Remarks on Free Entropy Dimension.- Yoshimichi Ueda: Notes on Treeability and Costs for Discrete Groupoids in Operator Algebra Framework.- Index

Rosenthal, Peter, Martinez-Avendano, Ruben A.

An Introduction to Operators on the Hardy-Hilbert Space

Series: Graduate Texts in Mathematics , Vol. 237
2006, Approx. 220 p., Hardcover.
ISBN: 0-387-35418-2
Due: September 2006

About this textbook

The subject of this book is operator theory on the Hardy space H^2, also called the Hardy-Hilbert space. This is a popular area, because the Hardy-Hilbert space is the most natural setting for operator theory. A reader who masters the material covered in this book will have acquired a firm foundation for the study of spaces of analytic functions and of operators on them. The goal is to provide an elementary introduction to this subject that will be readable by everyone who has understood introductory courses in complex analysis and in functional analysis. The exposition is clear and as instructive as possible, and the proofs are sufficiently beautiful that they will have a permanent place in mathematics.

This book is based on a graduate course that was taught at the University of Toronto. It should prove suitable as a textbook for beginning graduate students, or even to well-prepared advanced undergraduates. There are numerous exercises included at the end of each chapter, as well as a brief guide for further study.

Written for:

Graduate students in mathematics and engineering, mathematicians

Table of contents

Introduction.- The Unilateral Shift and Factorization of Functions.- Toeplitz Operators.- Hankel Operators.- Composition Operators.- Further reading.- References.- Notation Index.- Author Index.- Subject Index.

Jondeau, Eric, Rockinger, Michael, Poon, Ser-Huang

Financial Modeling Under Non-Gaussian Distributions

Series: Springer Finance
2006, Approx. 555 p., 129 illus., Hardcover.
ISBN: 1-84628-419-8
Due: September 2006

About this book

Practitioners and researchers who have handled financial market data know that asset returns do not behave according to the bell-shaped curve, associated with the Gaussian or normal distribution. Indeed, the use of Gaussian models when the asset return distributions are not normal could lead to a wrong choice of portfolio, the underestimation of extreme losses or mispriced derivative products. Consequently, non-Gaussian models and models based on processes with jumps, are gaining popularity among financial market practitioners.

Non-Gaussian distributions are the key theme of this book which addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. One of the main aims is to bridge the gap between the theoretical developments and the practical implementations of what many users and researchers perceive as "sophisticated" models or black boxes. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series, such as exchange and interest rates.

The authors have taken care to make the material accessible to anyone with a basic knowledge of statistics, calculus and probability, while at the same time preserving the mathematical rigor and complexity of the original models.

This book will be an essential reference for practitioners in the finance industry, especially those responsible for managing portfolios and monitoring financial risk, but it will also be useful for mathematicians who want to know more about how their mathematical tools are applied in finance, and as a text for advanced courses in empirical finance; financial econometrics and financial derivatives.

Written for:

Table of contents
Part I: Financial Markets and Financial Time Series.- Introduction. Statistical Properties of Financial Market Data. Functioning of Financial Markets and Theoretical Models for Returns. Part II: Econometric Modeling of Asset Returns.- Modeling Volatility. Modeling Higher Moments. Modeling Correlation. Extreme Value Theory. Part III: Applications of Non-Gaussian Econometrics.- Risk Management and VaR. Portfolio Allocation. Part IV: Option Pricing with Non-Gaussian Returns.-Fundamentals of Option Pricing. Non-Structural Option Pricing. Structural Option Pricing. Part V: Appendices on Option Pricing Mathematics.- Brownian Motion and Stochastic Calculus. Martingale and Changing Measure. Characteristic Functions and Fourier Transforms. Jump Processes.- References.- Index

Lim, Chjan, Nebus, Joseph

Vorticity, Statistical Mechanics, and Monte Carlo Simulation

Series: Applied Mathematical Sciences , Vol. 499
2006, Approx. 365 p., 50 illus., Hardcover.
ISBN: 0-387-35075-6
Due: September 2006

About this book

This book covers topics which include probability, statistical mechanics, Monte Carlo methods, spectral methods, discrete models for incompressible fluids, spin-lattice models, mesh generation and other numerical methods, geophysical models and mean field theory. The book will be a unique addition to the literature. It offers fresh insights into an important field and is certainly not a run-of-the-mill treatment of fluid mechanics or statistical mechanics.

Table of contents

Introduction.- Probability.- Statistical Mechanics.- The Monte Carlo Approach.- Spectral Methods.- Discrete Models in Fluids.- Spin-Lattice Models.- Monte Carlo Simulations.- Polyhedra and Ground States.- Mesh Generation.- Statistical Mechanics for a Vortex Gas.- Two-layer Quasi-geostrophic Models.- Barotropic Vorticity Dynamics.- Mean Field Theory.

Buchholz, D.; Iagolnitzer, D.; Moschella, U.; Boutet de Monvel, A. (Eds.)

Rigorous Quantum Field Theory
A Festschrift for Jacques Bros

Series: Progress in Mathematics , Vol. 251
2006, Approx. 330 p., Hardcover.
ISBN: 3-7643-7433-0
Due: September 2006

About this book

Jacques Bros has greatly advanced our present understanding of rigorous quantum field theory through numerous fundamental contributions. The impact of his work is also visible in several articles in this book. Quantum fields are considered as genuine mathematical objects, whose various properties and relevant physical interpretations have to be studied in a well-defined mathematical framework.

Key topics: Analytic structures of QFT, renormalization group methods, gauge QFT, stability properties and extension of the axiomatic framework, QFT on models of curved spacetimes, QFT on noncommutative Minkowski spacetime.

Written for:

Researchers in mathematical and theoretical physics

Keywords:

Minkowski space
Quantum field theory
Renormalization
Space-time
Yang-Mills algebras

Kromer, Ralf

Tool and Object
A History and Philosophy of Category Theory

Series: Science Networks. Historical Studies , Vol. 32
2006, Approx. 455 p., Hardcover.
ISBN: 3-7643-7523-X
Due: September 2006

About this book

Category theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its symbiotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance.

Written for:

Postgraduates and researchers in history of science; Mathematicians

Table of contents

Prologue.- Algebraic Topology.- Homological Algebra.- Algebraic Geometry.- Bourbaki.- Set Theory.- Category Theory as Foundation of Mathematics.- Appendix