03068nam a22004455i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001600153072001700169072002300186072001600209100007800225245012700303250001800430264006900448300004300517336002600560337002600586338003600612347002400648490005300672505023100725520118800956650002502144650002102169650002502190650002102215700007802236700007702314710003402391773002602425776003602451776003602487830005302523856004602576978-3-031-69926-9DE-He21320251030113109.0cr nn 008mamaa240927s2024    sz |    s    |||| 0|eng d  a97830316992697 a10.1007/978-3-031-69926-92doi 4aQA319-329.9 7aPBKF2bicssc 7aMAT0370002bisacsh 7aPBKF2thema1 aKordyukov, Yuri.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aPrincipal Symbol Calculus on Contact Manifoldsh[electronic resource] /cby Yuri Kordyukov, Fedor Sukochev, Dmitriy Zanin.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXIV, 156 p. 2 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aLecture Notes in Mathematics,x1617-9692 ;v23590 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.  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. 0aFunctional analysis. 0aOperator theory.14aFunctional Analysis.24aOperator Theory.1 aSukochev, Fedor.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut1 aZanin, Dmitriy.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303169925208iPrinted edition:z9783031699276 0aLecture Notes in Mathematics,x1617-9692 ;v235940uhttps://doi.org/10.1007/978-3-031-69926-9