Ordered vector spaces and cones made their debut in mathematics at the beginning of the twentieth century. They were developed in parallel (but from a different perspective) with functional analysis and operator theory. This book offers a modern perspectiv

Starting with few prerequisites beyond linear algebra, the author charts an expert course from Witt's classical theory of quadratic forms, quaternion and Clifford algebras, Artin-Schreier theory of formally real fields, and structural theorems on Witt ring

Describes the essence of the orbit method for non-experts and gives a detailed exposition of the method. This work can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists.

Operator theory is a significant part of many important areas of modern mathematics: functional analysis, differential equations, index theory, representation theory, and mathematical physics. This text covers the central themes of operator theory. It is suitable for graduate students who have had a standard course in functional analysis.

Classical groups, named so by Hermann Weyl, are groups of matrices or quotients of matrix groups by small normal subgroups. Thus the story begins, as Weyl suggested, with the general linear group GLULn(V) of all invertible linear transformations of a vector space V over a field F. All further groups discussed are either subgroups of GLULn(V) or closely related quotient groups. Most of the classical groups consist of invertible linear transformations that respect a bilinear form having some geometric significance, for example, a quadratic form, a symplectic form, and so forth.

The author presents, in great detail and with many examples, a basic collection of principles, techniques, and applications needed to conduct independent research in gauge theory and its use in geometry and topology. Complete and self-contained computations of the Seiberg-Witten invariants of most simply connected algebraic surfaces using only Witten's factorization method are included. Also given is a new approach to cutting and pasting Seiberg-Witten invariants, which is illustrated by examples such as the connected sum theorem, the blow-up formula, and a proof of a vanishing result of...

The first of two volumes on the qualitative theory of foliations, this comprehensive work has something to offer to a broad spectrum of readers, from beginners to advanced students and professional researchers. Offering illustrations and examples at varying degrees of difficulty, the text provides a full treatment of the theory of levels for foliated manifolds of codemension one.

This text concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces. The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations.

Perhaps uniquely among mathematical topics, complex analysis allows students to learn a thoroughly developed subject that is rich in both theory & applications. But for any of these profound results, the student is often left asking 'what does it mean?' In this text, Ullrich shows students how to think like an analyst.

A survey of asymptotic methods set in the applied research context of wave propagation. It stresses rigorous analysis in addition to formal manipulations. It is suitable for a beginning graduate course on asymptotic analysis in applied mathematics and is a