04102nam 2200625 450 991078885210332120170822144137.01-4704-0512-1(CKB)3360000000465090(EBL)3114221(SSID)ssj0000888975(PQKBManifestationID)11488376(PQKBTitleCode)TC0000888975(PQKBWorkID)10866999(PQKB)11151038(MiAaPQ)EBC3114221(RPAM)15190190(PPN)19541795X(EXLCZ)99336000000046509020080222h20082008 uy| 0engur|n|---|||||txtccrHeisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds /Raphaël S. PongeProvidence, Rhode Island :American Mathematical Society,[2008]©20081 online resource (150 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 906Description based upon print version of record.0-8218-4148-3 Includes bibliographical references (pages 131-134).""Contents""; ""Chapter 1. Introduction""; ""1.1. Heisenberg manifolds and their main differential operators""; ""1.2. Intrinsic approach to the Heisenberg calculus""; ""1.3. Holomorphic families of Î?[sub(H)]DO[sub(S)]""; ""1.4. Heat equation and complex powers of hypoelliptic operators""; ""1.5. Spectral asymptotics for hypoelliptic operators""; ""1.6. Weyl asymptotics and CR geometry""; ""1.7. Weyl asymptotics and contact geometry""; ""1.8. Organization of the memoir""; ""Chapter 2. Heisenberg manifolds and their main differential operators""; ""2.1. Heisenberg manifolds""""2.2. Main differential operators on Heisenberg manifolds""""Chapter 3. Intrinsic Approach to the Heisenberg Calculus""; ""3.1. Heisenberg calculus""; ""3.2. Principal symbol and model operators.""; ""3.3. Hypoellipticity and Rockland condition""; ""3.4. Invertibility criteria for sublaplacians""; ""3.5. Invert ibility criteria for the main differential operators""; ""Chapter 4. Holomorphic families of Î?[sub(H)]DO[sub(S)]""; ""4.1. Almost homogeneous approach to the Heisenberg calculus""; ""4.2. Holomorphic families of Î?[sub(H)]DO[sub(S)]""""4.3. Composition of holomorphic families of Î?[sub(H)]DO[sub(S)]""""4.4. Kernel characterization of holomorphic families of Î?]DO[sub(S)]""; ""4.5. Holomorphic families of Î?]DO[sub(S)] on a general Heisenberg manifold""; ""4.6. Transposes and adjoints of holomorphic families of Î?[sub(H)]DO[sub(S)]""; ""Chapter 5. Heat Equation and Complex Powers of Hypoelliptic Operators""; ""5.1. Pseudodifferential representation of the heat kernel""; ""5.2. Heat equation and sublaplacians""; ""5.3. Complex powers of hypoelliptic differential operators""; ""5.4. Rockland condition and the heat equation""""5.5. Weighted Sobolev Spaces""""Chapter 6. Spectral Asymptotics for Hypoelliptic Operators""; ""6.1. Spectral asymptotics for hypoelliptic operators""; ""6.2. Weyl asymptotics and CR geometry""; ""6.3. Weyl asymptotics and contact geometry""; ""Appendix A. Proof of Proposition 3.1.18""; ""Appendix B. Proof of Proposition 3.1.21""; ""Appendix. Bibliography""; ""References""Memoirs of the American Mathematical Society ;no. 906.Hypoelliptic operatorsSpectral theory (Mathematics)CalculusDifferentiable manifoldsHypoelliptic operators.Spectral theory (Mathematics)Calculus.Differentiable manifolds.515/.7242Ponge Raphael1972-1565965MiAaPQMiAaPQMiAaPQBOOK9910788852103321Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds3836135UNINA