LEADER 04102nam 2200625 450 001 9910788852103321 005 20170822144137.0 010 $a1-4704-0512-1 035 $a(CKB)3360000000465090 035 $a(EBL)3114221 035 $a(SSID)ssj0000888975 035 $a(PQKBManifestationID)11488376 035 $a(PQKBTitleCode)TC0000888975 035 $a(PQKBWorkID)10866999 035 $a(PQKB)11151038 035 $a(MiAaPQ)EBC3114221 035 $a(RPAM)15190190 035 $a(PPN)19541795X 035 $a(EXLCZ)993360000000465090 100 $a20080222h20082008 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHeisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds /$fRaphae?l S. Ponge 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2008] 210 4$dİ2008 215 $a1 online resource (150 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 906 300 $aDescription based upon print version of record. 311 $a0-8218-4148-3 320 $aIncludes bibliographical references (pages 131-134). 327 $a""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 I??[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"" 327 $a""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 I??[sub(H)]DO[sub(S)]""; ""4.1. Almost homogeneous approach to the Heisenberg calculus""; ""4.2. Holomorphic families of I??[sub(H)]DO[sub(S)]"" 327 $a""4.3. Composition of holomorphic families of I??[sub(H)]DO[sub(S)]""""4.4. Kernel characterization of holomorphic families of I??]DO[sub(S)]""; ""4.5. Holomorphic families of I??]DO[sub(S)] on a general Heisenberg manifold""; ""4.6. Transposes and adjoints of holomorphic families of I??[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"" 327 $a""5.5. Weighted Sobolev Spaces""""Chapter 6. Spectral Asymptotics for Hypoelliptic Operators""; ""6.1. Spectral asymptotics for hypoelliptic operators""; ""6.2. Weyl asymptotics and CR geometry""; ""6.3. Weyl asymptotics and contact geometry""; ""Appendix A. Proof of Proposition 3.1.18""; ""Appendix B. Proof of Proposition 3.1.21""; ""Appendix. Bibliography""; ""References"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 906. 606 $aHypoelliptic operators 606 $aSpectral theory (Mathematics) 606 $aCalculus 606 $aDifferentiable manifolds 615 0$aHypoelliptic operators. 615 0$aSpectral theory (Mathematics) 615 0$aCalculus. 615 0$aDifferentiable manifolds. 676 $a515/.7242 700 $aPonge$b Raphael$f1972-$01565965 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788852103321 996 $aHeisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds$93836135 997 $aUNINA