Bücher der Reihe Springer Monographs in Mathematics

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.

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.

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.

This book covers the properties and structure of positive linear maps of operator algebras into the bounded operators on Hilbert space.

This text is intended for a beginning graduate course on convexity methods for PDEs. The generality chosen by the author puts this under the classification of "functional analysis". The book contains new results and plenty of examples and exercises.

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 explores the fundamentals of total domination in graphs, the interplay with transversals in hypergraphs and the association with diameter-2-critical graphs. Includes several proofs, and a toolbox of proof techniques for attacking open problems.

This introduction to Shimura varieties covers key topics including non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; elliptic and modular curves over rings and more.

This book considers problems of optimization arising in the design of electromagnetic radiators and receivers, presenting a systematic general theory applicable to a wide class of structures. References to mathematics and engineering literature guide readers through the necessary mathematical background.

This is the revised and enlarged 2nd edition of the authors' original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory.

This book introduces the notion of an E-semigroup, a generalization of the known concept of E_O-semigroup. These objects are families of endomorphisms of a von Neumann algebra satisfying certain natural algebraic and continuity conditions. Its thorough approach is ideal for graduate students and research mathematicians.

The purpose of this text is to provide a self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, this one begins with the heat kernel on SL(2,C) associated to the invariant Laplacian, which is derived using spherical inversion.

Based on recent research papers, this book presents a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. It contains an extensive bibliography.

This book offers a clear and comprehensible introduction to incidence geometry, including such topics as projective and affine geometry and the theory of buildings and polar spaces. More than 200 figures make even complicated proofs accessible to the reader.

This comprehensive, encyclopedic text provides the reader - from the graduate student to the researcher/practitioner - with a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research.