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Elliptic Operators and Lie Groups

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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 noncommutative 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 subelliptic 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.
Request Code : ZLIB.IO17577892
Categories:
Year:
2022
Publisher:
Oxford University Press, USA
Language:
English
ISBN 10:
0198535910
ISBN 13:
9780198535911
ISBN:
0198535910, 9780198535911
Series:
Oxford Mathematical Monographs

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