LEADER 03054nam 22005415 450 001 9910890169603321 005 20240927130301.0 010 $a3-031-69926-2 024 7 $a10.1007/978-3-031-69926-9 035 $a(MiAaPQ)EBC31692114 035 $a(Au-PeEL)EBL31692114 035 $a(CKB)36213815000041 035 $a(DE-He213)978-3-031-69926-9 035 $a(EXLCZ)9936213815000041 100 $a20240927d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPrincipal Symbol Calculus on Contact Manifolds /$fby Yuri Kordyukov, Fedor Sukochev, Dmitriy Zanin 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (167 pages) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2359 311 $a3-031-69925-4 327 $aPreface -- Foreword by Nigel Higson -- Introduction -- Principal Symbol on the Heisenberg Group -- Equivariance of the Principal Symbol Under Heisenberg Diffeomorphisms -- Principal Symbol on Contact Manifolds -- Bibliography. 330 $aThis book develops a C*-algebraic approach to the notion of principal symbol on Heisenberg groups and, using the fact that contact manifolds are locally modeled by Heisenberg groups, on compact contact manifolds. Applying abstract theorems due to Lord, Sukochev, Zanin and McDonald, a principal symbol on the Heisenberg group is introduced as a homomorphism of C*-algebras. This leads to a version of Connes? trace theorem for Heisenberg groups, followed by a proof of the equivariant behavior of the principal symbol under Heisenberg diffeomorphisms. Using this equivariance and the authors? globalization theorem, techniques are developed which enable further extensions to arbitrary stratified Lie groups and, as a consequence, the notion of a principal symbol on compact contact manifolds is described via a patching process. Finally, the Connes trace formula on compact contact sub-Riemannian manifolds is established and a spectrally correct version of the sub-Riemannian volume is defined (different from Popp's measure). The book is aimed at graduate students and researchers working in spectral theory, Heisenberg analysis, operator algebras and noncommutative geometry. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2359 606 $aFunctional analysis 606 $aOperator theory 606 $aFunctional Analysis 606 $aOperator Theory 615 0$aFunctional analysis. 615 0$aOperator theory. 615 14$aFunctional Analysis. 615 24$aOperator Theory. 676 $a515.7 700 $aKordyukov$b Yuri$01769409 701 $aSukochev$b Fedor$01589038 701 $aZanin$b Dmitriy$01769410 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910890169603321 996 $aPrincipal Symbol Calculus on Contact Manifolds$94239486 997 $aUNINA