03438nam a22005415i 4500 978-3-031-69926-9 DE-He213 20251030113109.0 cr nn 008mamaa 240927s2024 sz | s |||| 0|eng d 9783031699269 978-3-031-69926-9 10.1007/978-3-031-69926-9 doi QA319-329.9 PBKF bicssc MAT037000 bisacsh PBKF thema Kordyukov, Yuri. author. aut http://id.loc.gov/vocabulary/relators/aut 85102 Principal Symbol Calculus on Contact Manifolds [electronic resource] / by Yuri Kordyukov, Fedor Sukochev, Dmitriy Zanin. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIV, 156 p. 2 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Lecture Notes in Mathematics, 1617-9692 ; 2359 Preface -- 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. This 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. Functional analysis. Operator theory. Functional Analysis. Operator Theory. Sukochev, Fedor. author. aut http://id.loc.gov/vocabulary/relators/aut 85103 Zanin, Dmitriy. author. aut http://id.loc.gov/vocabulary/relators/aut 85104 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031699252 Printed edition: 9783031699276 Lecture Notes in Mathematics, 1617-9692 ; 2359 75434 https://doi.org/10.1007/978-3-031-69926-9 ZDB-2-SMA ZDB-2-SXMS ZDB-2-LNM 63757 63757