Böcker i Encyclopaedia of Mathematical Sciences-serien

This book offers a comprehensive introduction to the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, K-theory, and quasidiagonality.

The twentieth-century view of the analysis of functions is dominated by the study of classes of functions. This volume of the Encyclopaedia covers the origins, development and applications of linear functional analysis, explaining along the way how one is led naturally to the modern approach.

This up-to-date survey of the whole field of topology is the flagship of the topology subseries of the Encyclopaedia. The book gives an overview of various subfields, beginning with the elements and proceeding right up to the present frontiers of research.

Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in mathematics and mathematical physics.

This book covers the modular invariant theory of finite groups. It details techniques for the computation of invariants for many modular representations of finite groups, especially the cyclic group of prime order, and includes many examples.

This newly translated addition to the literature provides a comprehensive treatment of the fundamentals of geophysical hydrodynamics -as expressed in Dolzhansky's four decades of ground-breaking work at the Moscow Institute of Physics and Technology.

Invariant Theory and Algebraic Transformation Groups VII

Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest.

Together with Theory of Operator Algebras I and III, this book presents the theory of von Neumann algebras and non-commutative integration focusing on the group of automorphisms and the structure analysis.

The only monograph on the topic, this book concerns geometric methods in the theory of differential equations with quadratic right-hand sides, closely related to the calculus of variations and optimal control theory. Based on the author's lectures, the book is addressed to undergraduate and graduate students, and scientific researchers.

From the reviews: "These three bulky volumes [EMS 124, 125, 127] [...] provide an introduction to this rapidly developing theory. [...] These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Acta Scientiarum Mathematicarum

Wholeheartedly recommended to every student and user of mathematics, this is an extremely original and highly informative essay on algebra and its place in modern mathematics and science.

Thus, m the space of states (phase space) is a subset M of an Euclidean space M . For continuous time systems, the evolution rule may be a differential eq- tion: to each state x G M one associates the speed and direction in which the system is going to evolve from that state.

What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool.

Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Catastrophe theory is accurately described as singularity theory and its (genuine) applications.

Devoted to finite-dimensional deterministic control systems governed by smooth ordinary differential equations, this book treats Mathematical Control Theory from a geometric viewpoint. Covers controllability, state and feedback equivalence and optimal control.

A brilliant and coherent summation of both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare.

[Gabriel and Roiter] are pioneers in this subject and they have included proofs for statements which in their opinions are elementary, those which will help further understanding and those which are scarcely available elsewhere. They attempt to take us up to the point where we can find our way in the original literature.

This book discusses knotted surfaces in 4-dimensional space and surveys many of the known results, including knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory.

By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q.

(1) 2a(x)cp(x) - Ix k(x, y)cp(y)dv(y) = f(x), Here (X, v) is a measure space with a-finite measure v, 2 is a complex parameter, and a, k, f are given (complex-valued) functions, which are referred to as the coefficient, the kernel, and the free term (or the right-hand side) of equation (1), respectively.

The first survey of its kind, written by internationally known, outstanding experts who developed substantial parts of the field.

Infinite series, and their analogues-integral representations, became funda mental tools in mathematical analysis, starting in the second half of the seven teenth century.

Intended for a wide range of readers, this book covers the main ideas of convex analysis and approximation theory.

This volume of the EMS contains four survey articles on analytic spaces. Starting from basic principles in several complex variables each article stretches out to current trends in research. Graduate students and researchers will find a useful addition in the extensive bibliography at the end of each article.

Classical harmonic analysis is an important part of modern physics and mathematics, comparable in its significance with calculus. Mathematical literature on harmonic analysis abounds in books of more or less abstract or concrete kind, but the lucky combination as in this volume can hardly be found.

This book is a survey of the most important directions of research in transcendental number theory. For readers with no specific background in transcendental number theory, the book provides both an overview of the basic concepts and techniques and also a guide to the most important results and references.