Bücher der Reihe Grundlehren der mathematischen Wissenschaften

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.

If we grant the legitimacy of the suggested precise replacements of the concept of algorithm and related concepts, then we can say that the mathematicians have shown by strictly mathematical methods that there exist mathematical problems which cannot be dealt with by the methods of calculating mathematics.

But if there is a sufficiently heavy accumulation of other boundary components, these can take over the distortion, and the mapping of the region itself remains conformal.

The aim of" the present monograph is two-fold: (a) to give a short account of the main results concerning the theory of random systems with complete connections, and (b) to describe the general learning model by means of random systems with complete connections.

Dantzig's development of linear programming into one of the most applicable optimization techniques has spread interest in the algebra of linear inequalities, the geometry of polyhedra, the topology of convex sets, and the analysis of convex functions.

This book contains a systematic exposition of the facts relating to partial differential equations with constant coefficients.

Of central importance in this book is the concept of modularity in lattices. These lattices are said to be M-sym metric, and their study forms an extension of the theory of modular lattices. We have a deep theory of parallelism in an affine matroid lattice, a special kind of matroid lattice.

The words "microdifferential systems in the complex domain" refer to seve ral branches of mathematics: micro local analysis, linear partial differential equations, algebra, and complex analysis.

This work grew out of Errett Bishop's fundamental treatise 'Founda tions of Constructive Analysis' (FCA), which appeared in 1967 and which contained the bountiful harvest of a remarkably short period of research by its author.

It is the author's aim to give a systematic account of the most im portant ideas, methods and results of the theory of topological vector spaces.