Books in the London Mathematical Society Monographs series

The aim of the book is to give necessary and sufficient conditions for a map to be stable. This is achieved in a wide range of dimensions via a detailed study of the geometry and topology of many classes of "generic" singularities.

The central part of the pluripotential theory is occupied by maximal plurisubharmonic functions and the generalized complex Monge-Ampere operator. The interplay between these two notions provides the focal point of this monograph, which explores classical properties of subharmonic and plurisubharmonic functions.

Although Lie polynomials first appeared at the turn of the century, there have been many recent developments especially from the point of view of representation theory. This book covers all aspects, with emphasis on the algebraic and combinatorial point of view as well as representation theory.

The book describes many specific classes of Banach algebras, including function algebras, group algebras, algebras of operators, C*=algebras, and radical Banach algebras; it is a compendium of results on these examples. The subject interweaves algebras, functional analysis, and complex analysis, and has a dash of set theory and logic; the background in all these areas is fully explained.

This work summarises the development of a classification system of finite p-groups. The authors provide a careful summary and explanation of the many and difficult original research papers on the co-class conjecture and the structure theorem, thus elucidating the background research for those new to the area as well as for experienced researchers.

Finite Coxeter groups and related structures arise naturally in several branches of mathematics, for example, Lie algebras or theory of knots and links. This is the first book which develops the character theory of finite Coxeter groups and Iwahori-Hecke algebras in a systematic way, ranging from classical results to recent developments.

Profinite groups are of interest to mathematicians in a variety of areas, including number theory, abstract groups, and analysis. This text provides an introduction to the subject and is designed to convey basic facts and enable readers to enhance their skills in manipulating profinite groups.

This book is a modern treatment of a classical area of operator theory. Written in a meticulous and detailed style, with the modern graduate student of analysis in mind, it contains many simplifications of existing literature. It is full of new results, as well as many illuminating examples. Carefully cross referenced throughout, it also includes an extensive list of the relevant literature.

A revised and expanded second edition of Reiter's Classical Harmonic Analysis and Locally Compact Groups (Clarendon Press 1968).

This work contains the first explicit construction of hidden structures (mantles and trains). The author shows how many infinite-dimensional groups are in fact only a small part of a much larger object, analogous to the way real numbers are embedded within complex numbers.

This monograph uses the language of homological algebra and sheaf theory to describe both classical results and recent developments in the spectral theory of linear operators. It draws together concepts from function theory and complex analytical geometry.

This advanced text expounds the established theory of ordered fields, and continues to develop a quite original theory of super-real fields. This theory has important applications in analysis and logic.

This invaluable reference tool is the first to present the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles the basic concepts, theory and methodologies needed to equip a beginning researcher in this area.

Highly topical and original monograph, introducing the author's work on the Riemann zeta function and its adelic interpretation of interest to a wide range of mathematicians and physicists.

This volume is concerned with the application of exponential sum techniques to a variety of problems in number theory, in particular the Riemann Zeta Function and the problem of estimating the number of lattice points in regions.

This book deals with the arithmetical properties of almost all real numbers. It brings together many different types of result (including normal numbers, Diophantine approximation and uniform distribution) never covered within the same volume before. By this approach interactions and common themes between different branches of the subject are revealed.

This is a reissue of a classic text previously published by the LMS, aimed at beginning postgraduate students in algebra and number theory. It gives a well-paced introduction to topics central to several active areas of mathematical research, and provides a very helpful background reference to researchers.

This book explores the application of mathematical analysis to problems of interpolation and engineering, including systems identification, and signal processing and sampling. It develops the mathematical background, and includes theoretical results and practical material on input design and identification algorithms. Many topics are presented for the first time.

Presents easy to understand proofs of some of the most difficult results about polynomials demonstrated by means of applications.

A comprehensive account of the restricted Burnside problem, including a new chapter on the highly acclaimed and recent work from E.I. Zelmanov.

This book explores in detail the connections between self-duality and integrability, and also the application of twistor techniques to integrable systems.

This concise introduction to the subject emphasizes the various classes of regular semigroups. More than 150 exercises, accompanied by references to the relevant research literature, direct readers to areas not explicitly covered in the text.

An introduction to the theory of existentially closed groups, this study is presented from a group theoretical, rather than a model theoretical, point of view.