Elliptic operators arise naturally in several different mathematical settings, notably in the representation theory of Lie groups, the study of evolution equations, and the examination of Riemannian manifolds. This book develops the basic theory of elliptic operators on Lie groups and thereby extends the conventional theory of parabolic evolution equations to a natural non-commutative context. In order to achieve this goal, the author presents a synthesis of ideas from partial differential equations, harmonic analysis, functional analysis, and the theory of Lie groups. He begins by discussing the abstract theory of general operators with complex coefficients before concentrating on the central case of second-order operators with real coefficients. A full discussion of second-order subellilptic operators is also given. Prerequisites are a familiarity with basic semigroup theory, the elementary theory of Lie groups, and a firm grounding in functional analysis as might be gained from the first year of a graduate course.
| ISBN: | 9780198535911 |
| Publication date: | 26th September 1991 |
| Author: | Derek W Head of Section, School of Mathemtical Sciences, Head of Section, School of Mathemtical Sciences, Australia Robinson |
| Publisher: | Clarendon Press an imprint of Oxford University Press |
| Format: | Hardback |
| Pagination: | 570 pages |
| Series: | Oxford Mathematical Monographs |
| Genres: |
Groups and group theory Functional analysis and transforms Differential calculus and equations |