Probability theory has become a convenient language and a useful tool in many areas of modern analysis. The main purpose of this book is to explore part of this connection concerning the relations between Brownian motion on a manifold and analytical aspects of differential geometry. A dominant theme of the book is the probabilistic interpretation of the curvature of a manifold.

This text is a comprehensive pedagogical presentation of the theory of representation of finite and compact Lie groups. It considers both the general theory and representation of specific groups. Representation theory is discussed on the following types of groups: finite groups of rotations, permutation groups, and classical compact semisimple Lie groups. Along the way, the structure theory of the compact semisimple Lie groups is exposed. This is aimed at research mathematicians and graduate students studying group theory.

This second part of this two-volume work 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 a clear account of the introductory portions of this important and technically difficult subject. Well supplied with exercises, the text assumes only basic measure theory and topology. The books present the possibility for the design of numerous courses aimed at different audiences.

Suitable for students in mathematics, physics, engineering, and computer science, this book explores contemporary approximation theory. It covers such topics as projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, and thin-plate splines.

Offers a geometric introduction to the homology of topological spaces and the cohomology of smooth manifolds. This title introduces a class of stratified spaces, so-called stratifolds. It derives basic concepts from differential topology such as Sard's the