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This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowle

Gives a description of analytical methods devised to study random matrices. This work reflects the developments in the field. It includes a coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals. It also presents Fredholm determinants and Painleve equations.

Serves as an introduction to the subject of Differentiable Manifolds and Riemannian Geometry for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. This book also reviews certain areas of advanced calculus that are necessary to understand the subject.

This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.