Bøger i Grundlehren der mathematischen Wissenschaften serien

Interactive particle systems is a branch of probability theory with close connections to mathematical physics and mathematical biology. This book takes three of the most important models in the area, and traces advances in our understanding of them since 1985. It explains and develops many of the most useful techniques in the field.

The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers.

The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems.

Gives a comprehensive account of the basic algebraic properties of the classical groups over rings. This book also includes a revised and expanded version of Dieudonne's classical theory over division rings. It analyses congruence subgroups, normal subgroups and quotient groups, and investigates connections with linear and hermitian K-theory.

Some Historical Background This book deals with the cohomology of groups, particularly finite ones. In number theory, group cohomology arose as a natural device for describing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field.

Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. He shows the fascination of the difficult Hardy-Littlewood theorems and of an unexpected simple proof, and extolls Wiener's breakthrough based on Fourier theory.

In recent years approximation theory and the theory of orthogonal polynomials have witnessed a dramatic increase in the number of solutions of difficult and previously untouchable problems.

We study the boundary behaviour of a conformal map of the unit disk onto an arbitrary simply connected plane domain. Then the conformal map has many unexpected properties, for instance almost all the boundary is mapped onto almost nothing and vice versa.

Arrangements have emerged independently asimportant objects in various fields of mathematics such ascombinatorics, braids, configuration spaces, representationtheory, reflection groups, singularity theory, and incomputer science and physics.

The theory of rings of quotients has its origin in the work of (j). In that case one defines the ring of fractions Q = A [S-l] as consisting of pairs (a, s) with aEA and SES, with the declaration that (a, s)=(b, t) if there exists UES such that uta = usb.

A monograph that deals with countable state Markov chains in both discrete time (Part I) and continuous time (Part II). [...]. It includes much of Kai Lai's fundamental work.

This is the first of a three-volume treatise on minimal surfaces. It covers the classical theory as well as existence results concerning boundary value problems for minimal surfaces, in particular results for Plateau's problem.

This is the second of a three-volume treatise on minimal surfaces. It deals with basic regularity results for minimal surfaces concerning their boundary behavior at Plateau boundaries and free boundaries.

This is the third of a three-volume treatise on minimal surfaces. It deals with geometric properties of minimal surfaces with free boundaries and with a priori gradient estimates for n-dimensional minimal surfaces, leading to various Bernstein-type theorems.

Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other subdisciplines. This book provides a comprehensive overview of major results, methods and ideas of convex and discrete geometry and its applications.

In addition to providing a self-contained introduction to p-adic lie groups, this volume discusses spaces of locally analytic functions as topological vector spaces, important to applications in representation theory.

This book is devoted to the systematic exposition of the contemporary theory of controlled Markov processes with discrete time parameter or in another termi nology multistage Markovian decision processes.

This presentation of the theory of hyperbolic conservation laws illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory.

That part of modular representation theory which is essentially the block theory of complex characters has not been included, as there are already monographs on this subject and others will shortly appear.

Since 1934 a multitude of papers devoted to inequalities have been published: in some of them new inequalities were discovered, in others classical inequalities ,vere sharpened or extended, various inequalities ,vere linked by finding their common source, while some other papers gave a large number of miscellaneous applications.

The applications of the theory not only permit integration of a series of diverse questions from many domains of mathematical analysis but also lead to significant new results on classical approximation theory, on the initial and boundary behavior of solutions of partial differential equations, and on the theory of singular integrals.

This book has grown out of a course of lectures I have given at the Eidgenossische Technische Hochschule, Zurich. I have to acknowledge my indebtedness to Professor Carl Ludwig Siegel, who has read the book, both in manuscript and in print, and made a number of valuable criticisms and suggestions.