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Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds
Raphaël S. Ponge, University of Toronto, ON, Canada
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Memoirs of the American Mathematical Society
2008; 134 pp; softcover
Volume: 194
ISBN-10: 0-8218-4148-3
ISBN-13: 978-0-8218-4148-8
List Price: US$69
Individual Members: US$41.40
Institutional Members: US$55.20
Order Code: MEMO/194/906
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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 Hörmander'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 and Taylor.

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
  • Appendix A. Proof of Proposition 3.1.18
  • Appendix B. Proof of Proposition 3.1.21
  • Bibliography
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