Analytic Pseudodifferential Operators for the Heisenberg Group and Local Solvability

Geller, Daryl

ISBN 10: 0691085641 / ISBN 13: 9780691085647

Published by Princeton University Press, 1990

About this Item

1990. Paperback. Paperback. Slight shelf wear. Very Good.

Seller Inventory # SIN0010038

Bibliographic Details

• Title: Analytic Pseudodifferential Operators for the Heisenberg Group and Local Solvability
• Publisher: Princeton University Press
• Publication Date: 1990
• Language: English
• ISBN 10: 0691085641
• ISBN 13: 9780691085647
• Binding: Soft cover
• Condition: Used - Very Good
• Seller catalogs:
  • Mathematics

About this title

Synopsis

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.

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