Memoirs of the American Mathematical Society 2008; 134 pp; softcover Volume: 194 ISBN10: 0821841483 ISBN13: 9780821841488 List Price: US$69 Individual Members: US$41.40 Institutional Members: US$55.20 Order Code: MEMO/194/906
 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 GoverGraham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of BealsGreiner 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
