Bøker i Oxford Mathematical Monographs-serien

This text is the first to deal with the general theory of traces and determinants of operators on manifolds in a broad context, encompassing a number of the principle applications and backed up by specific computations which set out in detail to newcomers the nuts-and-bolts of the basic theory.

This volume explores the connections between the geometry of mappings and many important areas of modern mathematics such as Harmonic and non-linear Analysis, the theory of Partial Differential Equations, Conformal Geometry and Topology. It provides a comprehensive and up to date account and an overview of the subject as a whole.

This second edition updates and expands the acclaimed first edition, adding a new chapter on a family of symmetric functions depending rationally on two parameters and also a chapter on zonal polynomials. It is available for the first time in paperback.

This book gives a complete and self-contained account of what is known about this subject and is written from a geometrical and analytical point of view, with quantum field theory very much in mind.

This book offers an extensive modern treatment of Sasakian geometry, which is of importance in many different fields in geometry and physics.

Building on the work of Ciarlet and Destuynder, this book provides a systematic coverage of these methods in multi-structures, for example, domains which are dependent on a small parameter e in such a way that the limit region consists of subsets of different space dimensions.

Succinct representation and fast access to large amounts of data are challenges of our time. This unique book suggests general approaches of 'complexity of descriptions'. It deals with a variety of concrete topics and bridges between them, while opening new perspectives and providing promising avenues for the 'complexity puzzle'.

Scattering theory deals with the interactions of waves with obstacles in their path, and low frequency scattering occurs when the obstacles involved are very small. This book gives an overview of the subject for graduates and researchers, for the first time unifying the theories covering acoustic, electromagnetic and elastic waves.

This text deals with fractal geometries which have features similar to ones of ordinary Euclidean spaces, while at the same time being different from Euclidean spaces in other ways. A basic type of feature being considered is the presence of Sobolev or Poincare inequalities.

Provides an accessible account to the modern study of the geometry of four-manifolds. This title is suitable for postgraduates and research workers. The central theme is that the appropriate geometrical tools for investigating these questions come from mathematical physics: the Yang-Mills theory and anti-self dual connections over four-manifolds.

Covers all the major areas including finitely generated soluble groups, soluble groups of finite rank, modules over group rings, algorithmic problems, applications of cohomology, finitely presented groups, whilst remaining fairly strictly within the boundaries of soluble group theory.

A wide-ranging introduction to a field of mathematics combining functional analysis with the perspectives of global geometry.

The study of the symmetric groups forms one of the basic building blocks of modern group theory. This book presents information currently known on the projective representations of the symmetric and alternating groups. Special emphasis is placed on the theory of Q-functions and skew Q-functions.

Summability methods are concerned with transforming series of numbers to other series. It is an area that has seen applications in number theory as well as in other parts of mathematics. This book covers both the theory and some of the applications of Borel summability.

This text provides an up-to-date account of Banach and locally convex algebras with emphasis on general theory, representations and homology. This approach leads Helemskii to consider topics not covered at this level in any other book.

This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.

This book lies at the interface between mathematics and quantum theory. It provides a mathematically precise development of certain heuristic ideas originated by Richard Feynman in a profoundly influential 1951 paper.

A general introduction to the initial value problem for Einstein's equations coupled to collisionless matter. The book contains a proof of future stability of models of the universe consistent with the current observational data and a discussion of the restrictions on the possible shapes of the universe imposed by observations.

This book presents a survey of the geometric quantization theory of Kostant and Souriau and was first published in 1980. It has been extensively rewritten and brought up to date, with the addition of many new examples.

Authored by leading scholars, this text presents the state of the art in multi-dimensional hyperbolic PDEs, with an emphasis on problems in which modern tools of analysis are used. Ordered in sections of gradually increasing difficulty and with an extensive bibliography, the text is ideal for graduates and researchers in applied mathematics.

This is a complete reworking of the out-of-print first volume of a three-volume treatise on finite projective spaces. There are numerous articles in journals, but this is the only extended work in the area. It also includes a comprehensive bibliography of more than 3000 items.

A unique monograph in a fast developing field of generalized thermoelasticity, an area of active research in continuum mechanics, focusing on thermoelasticity governed by hyperbolic equations, rather than on a wide range of continuum theories.

This work examines how the study of operator alegbras took a new turn with the introduction of subfactor theory, and how remarkable connections were found with knot theory, 3-manifolds, quantum groups and integrable systems in statistical mechanics and conformal theory. In the OXFORD MATHEMATICAL MONOGRAPHS series.

A simple introduction to several important fields of modern mathematics. The exposition is based on an interplay between hyperbolic geometry, stochastic calculus, special relativity and chaotic dynamics. It is suitable for anyone with some solid background in linear algebra, calculus, and probability theory.

Based in part on a lecture course, this book gives an authoritative and up-to-date overview of recent research on the behaviour of waves in crystalline solids. It covers aspects of plasticity, fracture, and nonlinear wave propagation.

The aim of this monograph is to present an account of the advances in the oscillation theory of delay differential equations - considering applications as diverse as the populations of blowflies, logistic equations in ecology and the survival of red blood cells in animals.

This study develops the theory of the complexity of the solution to differential and integral equations and discusses the relationship between the worst-case setting and two related problems - the average-case setting and the probalistic setting.

The central theme of this book is the study of self-dual connections on four-manifolds. The authors' aim is to present moduli space techniques applied to four-manifolds and to study vector bundles over four-manifolds whose structure group is SO(3).

This unique monograph brings together important material in the field of noncommutative rings and modules. It provides an up-to-date account of the topic of cyclic modules and the structure of rings which will be of particular interest to those working in abstract algebra and to graduate students who are exploring potential research topics.

This title presents the reader with a systematic introduction to a class of variational problems called 'free discontinuity problems'. The book bridges the gap between the research level and elementary courses on measure theory and calculus of variation at a level suitable for graduate students.