Abstract

The construction considered in these notes is based on a very simple idea. Let (A, G ) and (B, G ) be two group representations, for definiteness faithful and finite 1 2 dimensional, over an arbitrary field. We shall say that a faithful representation...

The marriage of analytic power to geometric intuition drives many of today's mathematical advances, yet books that build the connection from an elementary level remain scarce. This engaging introduction to geometric measure theory bridges analysis and...

This volume brings together lectures from an instructional meeting on spectral theory and geometry held under the auspices of the International Centre for Mathematical Sciences in Edinburgh. The contributions here come from world experts and many are...

Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions, the Dirichlet problem, harmonic measure, Green's functions, potentials and capacity. This is an introduction to the subject...

The first edition of this well known book was noted for its clear and accessible exposition of the basic theory of Hardy spaces from the concrete point of view (in the unit circle and the half plane). The intention was to give the reader, assumed to know...

This is an introduction to the analysis of metric and normed linear spaces for undergraduate students in mathematics. Assuming a basic knowledge of real analysis and linear algebra, the student is exposed to the axiomatic method in analysis and is shown...

Metric space topology, as the generalization to abstract spaces of the theory of sets of points on a line or in a plane, unifies many branches of classical analysis and is necessary introduction to functional analysis. Professor Copson's book, which is...

This textbook is an introduction to the techniques of summing and nuclear norms. The author's aim is to present a clear and simple account of these ideas and to demonstrate the power of their application to a variety of Banach space questions. The style...

This unique book develops the classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, in rather a novel way to provide a unifying framework in which they can be studied. The author focuses on...

This book presents a theory motivated by the spaces LP, 0 p < l. These spaces are not locally convex, so the methods usually encountered in linear analysis (particularly the Hahn-Banach theorem) do not apply here. Questions about the size of the dual...

This treatise deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioural and social sciences. The authors have chosen to emphasize applications, though not...

Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal...

This work has arisen from lecture courses given by the authors on important topics within functional analysis. The authors, who are all leading researchers, give introductions to their subjects at a level ideal for beginning graduate students, and others...

In this book, first published in 2003, the reader is provided with a tour of the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, together with some...

This book provides a clear exposition of the flourishing field of fixed point theory. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are established for several classes...

Integration has a long history: its roots can be traced as far back as the ancient Greeks. The first genuinely rigorous definition of an integral was that given by Riemann, and further (more general, and so more useful) definitions have since been given...

In this tract, Dr Ruston presents analogues for operators on Banach spaces of Fredholm's solution of integral equations of the second kind. Much of the presentation is based on research carried out over the last twenty-five years and has never appeared...

Certain functions, capable of expansion only as a divergent series, may nevertheless be calculated with great accuracy by taking the sum of a suitable number of terms. The theory of such asymptotic expansions is of great importance in many branches of...

Dr Burkill gives a straightforward introduction to Lebesgue's theory of integration. His approach is the classical one, making use of the concept of measure, and deriving the principal results required for applications of the theory.A straightforward...

This book presents a mathematical introduction to the theory of orthogonal wavelets and their uses in analysing functions and function spaces, both in one and in several variables. Starting with a detailed and self contained discussion of the general...

This is an introductory text intended to give the non-specialist a comprehensive insight into the science of biotransformations. The book traces the history of biotransformations, clearly spells out the pros and cons of conducting enzyme-mediated versus...

These lecture notes are intended as a non-technical overview of scattering theory. The point of view adopted throughout is that scattering theory provides a parameterization of the continuous spectrum of an elliptic operator on a complete manifold with...

The Computer Algebra and Differential Equations meeting held in France in June 1992 (CADE-92) was the third of a series of biennial workshops devoted to recent developments in computer algebra systems. This book contains selected papers from that meeting...

This volume reflects the progress made in many branches of recent research in Banach space theory. It is based on a conference attended by most of the leading figures in the area, and is intended to illustrate the interplay of Banach space theory with...

This volume, dedicated to Professor A. Plans, concentrates on some important and contemporary themes in Banach space theory. The articles are by leading researchers and cover topics such as sequences, operators, eigenvalues, s-numbers and projection...

This book is concerned with the modern theory of Fourier series. Treating developments since Zygmund's classic study, the authors begin with a thorough discussion of the classical one-dimensional theory from a modern perspective. The text then takes up...

Convex geometry is at once simple and amazingly rich. While the classical results go back many decades, during that previous to this book's publication in 1999, the integral geometry of convex bodies had undergone a dramatic revitalization, brought about...

This 2010 book was the first devoted to the theory of p-adic wavelets and pseudo-differential equations in the framework of distribution theory. This relatively recent theory has become increasingly important in the last decade with exciting applications...

In these notes the abstract theory of analytic one-parameter semigroups in Banach algebras is discussed, with the Gaussian, Poisson and fractional integral semigroups in convolution Banach algebras serving as motivating examples. Such semigroups are...

This Tract presents an elaboration of the notion of 'contiguity', which is a concept of 'nearness' of sequences of probability measures. It provides a powerful mathematical tool for establishing certain theoretical results with applications in...

This book is a self-contained account of knowledge of the theory of nonlinear superposition operators: a generalization of the notion of functions. The theory developed here is applicable to operators in a wide variety of function spaces, and it is here...

This unique book develops the classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, in rather a novel way to provide a unifying framework in which they can be studied. The author focuses on...

Entropy quantities are connected with the 'degree of compactness' of compact or precompact spaces, and so are appropriate tools for investigating linear and compact operators between Banach spaces. The main intention of this Tract is to study the...

This tract gives a clear exposition of the elementary theory of Fourier transforms, so arranged as to give easy access to the recently developed abstract theory of Fourier transforms on a locally compact group. (This latter subject has important...

This is an introduction to p-adic analysis which is elementary yet complete and which displays the variety of applications of the subject. Dr Schikhof is able to point out and explain how p-adic and 'real' analysis differ. This approach guarantees the...

This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representations of a reductive algebraic group over a local field in terms of the complex dual group and the...

The theme of this work, the logarithmic integral, lies athwart much of twentieth-century analysis. It is a thread connecting many apparently separate parts of the subject, and so is a natural point at which to begin a serious study of real and complex...

Linear systems can be regarded as a causal shift-invariant operator on a Hilbert space of signals, and by doing so this book presents an introduction to the common ground between operator theory and linear systems theory. The book therefore includes...

The study of free resolutions is a core and beautiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas...

The distribution of the eigenvalues of differential operators has long fascinated mathematicians. Advances have shed light upon classical problems in this area, and this book presents a fresh approach, largely based upon the results of the authors. The...