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Semi-Classical Analysis (Paperback)
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Semi-Classical Analysis (Paperback)
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There are a number of excellent texts available on semi-classical
analysis. The focus of the present monograph, however, is an aspect
of the subject somewhat less systematically developed in other
texts: In semi-classical analysis, many of the basic results
involve asymptotic expansions in which the terms can be computed by
symbolic techniques, and the focus of this monograph is the "symbol
calculus" created thus. In particular, the techniques involved in
this symbolic calculus have their origins in symplectic geometry,
and the first seven chapters of the present work are a discussion
of this underlying symplectic geometry. Another feature which
differentiates this monograph from other texts is an emphasis on
the global aspects of the subject: A considerable amount of time is
spent here showing that the objects studied are
coordinate-invariant and hence make sense on manifolds. Wherever
possible, intrinsic coordinate-free descriptions of these objects
are given. Topics discussed include wave and heat trace formulas
for globally defined semi-classical differential operators on
manifolds, and equivariant versions of these results involving Lie
group actions.
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