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
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.
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
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.
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
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