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Author : Yuri Kordyukov
Release :
Genre :
Kind : eBook
Book Rating : 262/5 ( reviews)
Book Synopsis Principal Symbol Calculus on Contact Manifolds by : Yuri Kordyukov
Download or read book Principal Symbol Calculus on Contact Manifolds written by Yuri Kordyukov. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yuri Kordyukov
Release : 2024-10-30
Genre : Mathematics
Kind : eBook
Book Rating : 252/5 ( reviews)
Book Synopsis Principal Symbol Calculus on Contact Manifolds by : Yuri Kordyukov
Download or read book Principal Symbol Calculus on Contact Manifolds written by Yuri Kordyukov. This book was released on 2024-10-30. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Richard Beals
Release : 2016-03-02
Genre : Mathematics
Kind : eBook
Book Rating : 397/5 ( reviews)
Book Synopsis Calculus on Heisenberg Manifolds. (AM-119), Volume 119 by : Richard Beals
Download or read book Calculus on Heisenberg Manifolds. (AM-119), Volume 119 written by Richard Beals. This book was released on 2016-03-02. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Calculus on Heisenberg Manifolds. (AM-119), Volume 119, will be forthcoming.
Author : Veronique Fischer
Release : 2016-03-08
Genre : Mathematics
Kind : eBook
Book Rating : 586/5 ( reviews)
Book Synopsis Quantization on Nilpotent Lie Groups by : Veronique Fischer
Download or read book Quantization on Nilpotent Lie Groups written by Veronique Fischer. This book was released on 2016-03-08. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.
Author : Raphael Ponge
Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 483/5 ( reviews)
Book Synopsis Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds by : Raphael Ponge
Download or read book Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds written by Raphael Ponge. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner andTaylor.
