Bøger i Springer Monographs in Mathematics serien

A collection of the various old and new results, centered around the following simple observation of J L Walsh. This book is particularly useful for researchers in approximation and interpolation theory.

Function Algebras on Finite Sets gives a broad introduction to the subject, leading up to the cutting edge of research. The general concepts of the Universal Algebra are given in the first part of the book, to familiarize the reader from the very beginning on with the algebraic side of function algebras.

Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. The book also contains some examples of computations and applications.

This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields.

This is the first treatment in book format of proof-theoretic transformations - known as proof interpretations - that focuses on applications to ordinary mathematics.

This clearly written text is the first book on unitals embedded in finite projective planes. It provides a thorough survey of the research literature on embedded unitals. The book is well-structured with excellent diagrams and a comprehensive bibliography.

Here is a key text on the subject of representation theory in finite groups. The pages of this excellent little book, prepared by Rafael Stekolshchik, contain a number of new proofs relating to Coxeter Transformations and the McKay Correspondence. Ponomarev, as well as material from Coxeter and McKay themselves.

The problem of spectral asymptotics, in particular the problem of the asymptotic dis tribution of eigenvalues, is one of the central problems in the spectral theory of partial differential operators; to provide furt her progress and only a couple of not very exciting problems remained to be solved.

In the theory of operator algebras, a C*-algebra A that turns out to be small in this sense tradition ally is enlarged to its (universal) enveloping von Neumann algebra A". This works well since von Neumann algebras are in many respects richer and, from the Banach space point of view, A" is nothing other than the second dual space of A.

Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.

It reviews the basic theories and methods, with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications, and provides the necessary preparation for almost all important aspects in contemporary studies.

An attractive book on the intersection of analysis and numerical analysis, deriving classical boundary integral equations arising from the potential theory and acoustics. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.

This monograph presents a self contained mathematical treatment of the initial value problem for shock wave solutions of the Einstein equations in General Relativity. It has a clearly outlined goal: proving a certain local existence theorem. The author is a well regarded expert in this area.

This book examines algebraic number theory and the theory of semisimple algebras. It covers classification over an algebraic number field and classification over the ring of algebraic integers.

This monograph is concerned with the basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type. It focuses on major results in recent decades.

This book presents the basic methods of regular perturbation theory of Hamiltonian systems in an accessible fashion. It discusses all main aspects of the basic modern theory of perturbed Hamiltonian systems, and most results include complete proofs.

It covers classical functional equations, difference and differential equations, polynomial ideals, digital filtering and polynomial hypergroups, giving unified treatment of several different problems.

This book presents results on well-posedness, regularity and long-time behavior of non-linear dynamic plate (shell) models described by von Karman evolutions. The coverage is comprehensive and elf-contained, and the theory applies to many similar dynamics.

This text covers the mathematical theory of linear elliptic equations and systems and the related function spaces framework. It provides an introduction to the modern theory of partial differential equations, the theory of weak solutions and related topics.

For the most part the authors are concerned with SLn(R) and with invariant differential operators, the invarinace being with respect to various subgroups. To a large extent, this book carries out the general results of Harish-Chandra.

This book gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. Its main goal is to provide complexity estimates by tracking numerically invariants of the structures that may occur.

Self-contained presentation: from elementary material to state-of-the-art research; Much of the theory in book-form for the first time; Connections are made between probability and other areas of mathematics, engineering and mathematical physics

Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences.

The central theme of this book is the restoration of Poincare duality on stratified singular spaces by using Verdier-self-dual sheaves such as the prototypical intersection chain sheaf on a complex variety.

Variational and boundary integral equation techniques are two of the most useful methods for solving time-dependent problems described by systems of equations of the form 2 ?

The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. This book provides an overview of "generic chaining", a completely natural variation on the ideas of Kolmogorov.

This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. It shows that hypergeometric integrals generally satisfy holonomic system of linear differential equations.