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9780821841488

Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds

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  • ISBN13:

    9780821841488

  • ISBN10:

    0821841483

  • Format: Paperback
  • Copyright: 2008-06-29
  • Publisher: Amer Mathematical Society

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Summary

This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner andTaylor.

Table of Contents

Introduction
Heisenberg manifolds and their main differential operators
Intrinsic approach to the Heisenberg calculus
Holomorphic families of $\mathbf{\Psi_{H}}$DOs
Heat equation and complex powers of hypoelliptic operators
Spectral asymptotics for hypoelliptic operators
Proof of Proposition 3.1.18
Proof of Proposition 3.1.21
Bibliography
Table of Contents provided by Publisher. All Rights Reserved.

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