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Analytic Pseudodifferential Operators for the Heisenberg Group and Local Solvability. (MN-37) (Hardcover)
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Analytic Pseudodifferential Operators for the Heisenberg Group and Local Solvability. (MN-37) (Hardcover)
Series: Mathematical Notes
Expected to ship within 10 - 15 working days
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Many of the operators one meets in several complex variables, such
as the famous Lewy operator, are not locally solvable.
Nevertheless, such an operator L can be thoroughly studied if one
can find a suitable relative parametrix--an operator K such that LK
is essentially the orthogonal projection onto the range of L. The
analysis is by far most decisive if one is able to work in the real
analytic, as opposed to the smooth, setting. With this motivation,
the author develops an analytic calculus for the Heisenberg group.
Features include: simple, explicit formulae for products and
adjoints; simple representation-theoretic conditions, analogous to
ellipticity, for finding parametrices in the calculus; invariance
under analytic contact transformations; regularity with respect to
non-isotropic Sobolev and Lipschitz spaces; and preservation of
local analyticity. The calculus is suitable for doing analysis on
real analytic strictly pseudoconvex CR manifolds. In this context,
the main new application is a proof that the Szego projection
preserves local analyticity, even in the three-dimensional setting.
Relative analytic parametrices are also constructed for the adjoint
of the tangential Cauchy-Riemann operator. Originally published in
1990. The Princeton Legacy Library uses the latest print-on-demand
technology to again make available previously out-of-print books
from the distinguished backlist of Princeton University Press.
These editions preserve the original texts of these important books
while presenting them in durable paperback and hardcover editions.
The goal of the Princeton Legacy Library is to vastly increase
access to the rich scholarly heritage found in the thousands of
books published by Princeton University Press since its founding in
1905.
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