Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds / Raphael Ponge

Author: Ponge, Raphael, 1972-
Published: Providence, R.I. : American Mathematical Society, 2008.
Physical Description: vii, 134 pages ; 25 cm.

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Series

Memoirs of the American Mathematical Society ; v. 194, no. 906

Contents

Introduction -- Heisenberg manifolds and their main differential operators -- Intrinsic approach to the Heisenberg calculus -- Holomorphic families of HDOs -- Heat equation and complex powers of hypoelliptic operators -- Spectral asymptotics for hypoelliptic operators -- Weyl asymptotics and CR geometry -- Weyl asymptotics and contact geometry -- Organization of the memoir -- Heisenberg manifolds and their main differential operators -- Heisenberg manifolds -- Main differential operators on Heisenberg manifolds -- Intrinsic approach to the Heisenberg calculus -- Heisenberg calculus -- Principal symbol and model operators -- Hypoellipticity and Rockland condition -- Invertibility criteria for sublaplacians -- Invertibility criteria for the main differential operators -- Holomorphic families of HDOs -- Almost homogeneous approach to the Heisenberg calculus -- Holomorphic families of HDOs -- Composition of holomorphic families of HDOs -- Kernel characterization of holomorphic families of HDOs -- Holomorphic families of HDOs on a general Heisenberg manifold -- Ttransposes and adjoints of holomorphic families of HDOs -- Heat equation and complex powers of hypoelliptic operators -- Pseudodifferential representation of the heat kernel -- Heat equation and sublaplacians -- Complex powers of hypoelliptic differential operators -- Rockland condition and the heat equation -- Weighted Sobolev spaces -- Spectral asymptotics for hypoelliptic operators -- Spectral asymptotics for hypoelliptic operators -- Weyl asymptotics and CR geometry -- Weyl asymptotics and contact geometry.

Subject(s)

ISBN

9780821841488 (alk. paper)
0821841483 (alk. paper)

Bibliography Note

Includes bibliographical references.

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