Kordyukov, Yuri. creator author. aut http://id.loc.gov/vocabulary/relators/aut Sukochev, Fedor. author. aut http://id.loc.gov/vocabulary/relators/aut Zanin, Dmitriy. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text sz 2024 1st ed. 2024. monographic eng

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access XIV, 156 p. 2 illus. online resource. 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. 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. by Yuri Kordyukov, Fedor Sukochev, Dmitriy Zanin. Functional analysis Operator theory Functional Analysis Operator Theory QA319-329.9 9783031699269 https://doi.org/10.1007/978-3-031-69926-9 https://doi.org/10.1007/978-3-031-69926-9 240927 20251030113109.0 978-3-031-69926-9