Calculus on Heisenberg Manifolds. (AM-119), Volume 119

by Richard Beals, Peter Charles Greiner

Overview

A classic treatment of the hypoelliptic calculus on Heisenberg Manifolds

The classical pseudodifferential calculus is well adapted to detailed study of elliptic operators such as the Laplacian associated to the De Rham complex. This book develops a full asymptotic calculus adapted to certain second order operators which are hypoelliptic but not elliptic. The motivating example is the operator _b associated to the ∂_b-complex on a CR-manifold. Like the Laplacian, _b is a natural operator of intrinsic interest, a prototype of a general class, and a test case. Principal terms of parametrices and other operators associated to _b are calculated on both the symbol side and the kernel side. It is hoped that this viewpoint on pseudodifferential operators will be fruitful in attacking other nonelliptic problems, including more degenerate cases of _b.

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Product Details

ISBN-13:	9780691085012
Publisher:	Princeton University Press
Publication date:	08/21/1988
Series:	Annals of Mathematics Studies , #119
Pages:	208
Product dimensions:	6.00(w) x 9.00(h) x (d)

About the Author

Richard Beals is professor emeritus of mathematics at Yale University. Peter Greiner is professor emeritus of mathematics at the University of Toronto.

Table of Contents

• Frontmatter, pg. i
• Contents, pg. vii
• Preface, pg. ix
• Introduction, pg. 1
• Chapter 1. The Model Operators, pg. 11
• Chapter 2. Inverting the Model Operator, pg. 23
• Chapter 3. Pseudodifferential Operators on Heisenberg Manifolds, pg. 80
• Chapter 4. Application to the ∂̅b - Complex, pg. 151
• Bibliography, pg. 181
• Index of Terminology, pg. 189
• List of Notation, pg. 192