Bøger i Graduate Studies in Mathematics serien

Gives an introduction to the theory of the integral (called the 'generalized Riemann integral' or the 'Henstock-Kurzweil integral') that corrects the defects in the classical Riemann theory and both simplifies and extends the Lebesgue theory of integration. This book includes a study of measure theory as an application of the integral.

Presents main theorems about class fields of algebraic number fields. This book features calculations with quadratic fields that show the use of the norm residue symbol.

A guide to the qualitative theory of foliations. It features topics including: analysis on foliated spaces, characteristic classes of foliations and foliated manifolds. It is suitable as a supplementary text for a topics course at the advanced graduate level.

Suitable for a first year graduate course on global analysis, this title proves the basics of Fourier transforms, Sobolev theory and interior regularity at the same time as symbol calculus, culminating in beautiful results in global analysis, real and complex.

Deals with finite-alphabet stationary processes, which are important in physics, engineering, and data compression. This book gives a careful presentation of the many models for stationary finite-alphabet processes that have been developed in probability theory, ergodic theory, and information theory.

Presents an introduction to set theory for beginning graduate students who want to get a grounding in those aspects of set theory used extensively throughout other areas of mathematics. This book contains topics that include formal languages and models, the power and limitation of the Axiomatic Method, and the Axiom of Choice.

Presents an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide an account of the introductory portions of this important and technically difficult subject.

Intended for graduate students who have completed standard courses in linear algebra and abstract algebra, this title provides a single source for the basic facts about the classical groups and also includes the required geometrical background information from the first principles.

Presents an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide an account of the introductory portions of this important and technically difficult subject.

Explains the problems that must be resolved in order to procure a rigorous development of the calculus and shows the student how to deal with those problems. Starting with the real line, this book also covers finite-dimensional spaces and metric spaces.

Probability theory has become a convenient language and a useful tool in many areas of modern analysis. This book intends to explore part of this connection concerning the relations between Brownian motion on a manifold and analytical aspects of differential geometry. It begins with a review of stochastic differential equations on Euclidean space.

Presents an account of noncommutative Noetherian rings. This book covers the major developments from the 1950s, stemming from Goldie's theorem and onward, including applications to group rings, enveloping algebras of Lie algebras, PI rings, differential operators, and localization theory.