Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds
By: Raphael Ponge.
Series: Memoirs of the American Mathematical Society -- v. 194, no. 906
Publisher: American Mathematical Society
Published: 2008
Place of publication: Providence, R.I
Language: eng
ISBN-13: 9780821841488
Subjects: Hypoelliptic operators; Spectral theory (Mathematics); Calculus; Differentiable manifolds
Notes: Includes bibliographical references.
Table of contents: title: Introduction; title: Heisenberg manifolds and their main differential operators; title: Intrinsic approach to the Heisenberg calculus; title: Holomorphic families of HDOs; title: Heat equation and complex powers of hypoelliptic operators; title: Spectral asymptotics for hypoelliptic operators; title: Weyl asymptotics and CR geometry; title: Weyl asymptotics and contact geometry; title: Organization of the memoir; title: Heisenberg manifolds and their main differential operators; title: Heisenberg manifolds; title: Main differential operators on Heisenberg manifolds; title: Intrinsic approach to the Heisenberg calculus; title: Heisenberg calculus; title: Principal symbol and model operators; title: Hypoellipticity and Rockland condition; title: Invertibility criteria for sublaplacians; title: Invertibility criteria for the main differential operators; title: Holomorphic families of HDOs; title: Almost homogeneous approach to the Heisenberg calculus; title: Holomorphic families of HDOs; title: Composition of holomorphic families of HDOs; title: Kernel characterization of holomorphic families of HDOs; title: Holomorphic families of HDOs on a general Heisenberg manifold; title: Ttransposes and adjoints of holomorphic families of HDOs; title: Heat equation and complex powers of hypoelliptic operators; title: Pseudodifferential representation of the heat kernel; title: Heat equation and sublaplacians; title: Complex powers of hypoelliptic differential operators; title: Rockland condition and the heat equation; title: Weighted Sobolev spaces; title: Spectral asymptotics for hypoelliptic operators; title: Spectral asymptotics for hypoelliptic operators; title: Weyl asymptotics and CR geometry; title: Weyl asymptotics and contact geometry.