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Analytic pseudodifferential operators for the Heisenberg group and local solvability

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Analytic pseudodifferential operators for the Heisenberg group and local solvability Cover

 

Synopses & Reviews

Publisher Comments:

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 paperback editions preserve the original texts of these important books while presenting them in durable paperback 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.

Book News Annotation:

Develops a calculus of pseudodifferential operators for the Heisenberg group in the (real) analytic setting, and applies this calculus to the study of certain operators arising in several complex variables. No index.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Description:

Includes bibliographical references (p. [489]-495).

Product Details

ISBN:
9780691085647
Publisher:
Princeton University Press
Location:
Princeton, N.J. :
Author:
Geller, Daryl
Subject:
General
Subject:
Functions of several complex variables
Subject:
Pseudodifferential operators.
Subject:
Solvable groups.
Subject:
Calculus
Subject:
Mathematics
Edition Description:
Trade paper
Series:
Mathematical Notes
Series Volume:
37
Publication Date:
19900221
Binding:
Paperback
Illustrations:
Yes
Pages:
504
Dimensions:
9.22x6.15x1.12 in. 1.52 lbs.

Related Subjects

Science and Mathematics » Biology » General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Real Analysis

Analytic pseudodifferential operators for the Heisenberg group and local solvability
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Product details 504 pages Princeton University Press,1990. - English 9780691085647 Reviews:
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