Heisenberg Calculus And Spectral Theory Of Hypoelliptic Operators On Heisenberg Manifolds
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Heisenberg Calculus And Spectral Theory Of Hypoelliptic Operators On Heisenberg Manifolds
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Author : Raphael Ponge
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Heisenberg Calculus And Spectral Theory Of Hypoelliptic Operators On Heisenberg Manifolds written by Raphael Ponge and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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.
Principal Symbol Calculus On Contact Manifolds
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Author : Yuri Kordyukov
language : en
Publisher: Springer Nature
Release Date : 2024-09-26
Principal Symbol Calculus On Contact Manifolds written by Yuri Kordyukov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-26 with Mathematics categories.
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.
Motives Quantum Field Theory And Pseudodifferential Operators
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Author : Alan L. Carey
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Motives Quantum Field Theory And Pseudodifferential Operators written by Alan L. Carey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This volume contains articles related to the conference ``Motives, Quantum Field Theory, and Pseudodifferntial Operators'' held at Boston University in June 2008, with partial support from the Clay Mathematics Institute, Boston University, and the National Science Foundation. There are deep but only partially understood connections between the three conference fields, so this book is intended both to explain the known connections and to offer directions for further research. In keeping with the organization of the conference, this book contains introductory lectures on each of the conference themes and research articles on current topics in these fields. The introductory lectures are suitable for graduate students and new Ph.D.'s in both mathematics and theoretical physics, as well as for senior researchers, since few mathematicians are expert in any two of the conference areas. Among the topics discussed in the introductory lectures are the appearance of multiple zeta values both as periods of motives and in Feynman integral calculations in perturbative QFT, the use of Hopf algebra techniques for renormalization in QFT, and regularized traces of pseudodifferential operators. The motivic interpretation of multiple zeta values points to a fundamental link between motives and QFT, and there are strong parallels between regularized traces and Feynman integral techniques. The research articles cover a range of topics in areas related to the conference themes, including geometric, Hopf algebraic, analytic, motivic and computational aspects of quantum field theory and mirror symmetry. There is no unifying theory of the conference areas at present, so the research articles present the current state of the art pointing towards such a unification.
The Heisenberg Group
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Author : Gerald B. Folland
language : en
Publisher: American Mathematical Society
Release Date : 2025-04-15
The Heisenberg Group written by Gerald B. Folland and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-15 with Mathematics categories.
Over the past hundred years, the Heisenberg group has been recognized as an important object in several areas of mathematics, including group representation theory, mathematical physics, complex analysis in several variables, partial differential equations, and differential geometry. This book presents a concise and readable introduction to all these aspects, together with brief descriptions of further research in the area over the past few decades. The author also provides copious references. Prerequisites for the potential reader are a graduate-level course in modern real analysis, plus the rudiments of functional analysis, Fourier analysis, differential geometry, and Lie groups.
Twisted Pseudodifferential Calculus And Application To The Quantum Evolution Of Molecules
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Author : Andr Martinez
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-06-05
Twisted Pseudodifferential Calculus And Application To The Quantum Evolution Of Molecules written by Andr Martinez and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-05 with Mathematics categories.
The authors construct an abstract pseudodifferential calculus with operator-valued symbol, suitable for the treatment of Coulomb-type interactions, and they apply it to the study of the quantum evolution of molecules in the Born-Oppenheimer approximation, in the case of the electronic Hamiltonian admitting a local gap in its spectrum. In particular, they show that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitely. In addition, they study the propagation of certain wave packets up to long time values of Ehrenfest order.
New Trends In Sub Riemannian Geometry
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Author : Fabrice Baudoin
language : en
Publisher: American Mathematical Society
Release Date : 2025-01-27
New Trends In Sub Riemannian Geometry written by Fabrice Baudoin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-27 with Mathematics categories.
This volume contains the proceedings of the AMS-EMS-SMF Special Session on Sub-Riemannian Geometry and Interactions, held from July 18–20, 2022, at the Université de Grenoble-Alpes, Grenoble, France. Sub-Riemannian geometry is a generalization of Riemannian one, where a smooth metric is defined only on a preferred subset of tangent directions. Under the so-called Hörmander condition, all points are connected by finite-length curves, giving rise to a well-defined metric space. Sub-Riemannian geometry is nowadays a lively branch of mathematics, connected with probability, harmonic and complex analysis, subelliptic PDEs, geometric measure theory, optimal transport, calculus of variations, and potential analysis. The articles in this volume present some developments of a broad range of topics in sub-Riemannian geometry, including the theory of sub-elliptic operators, holonomy, spectral theory, and the geometry of the exponential map.
The Stable Manifold Theorem For Semilinear Stochastic Evolution Equations And Stochastic Partial Differential Equations
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Author : Salah-Eldin Mohammed
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
The Stable Manifold Theorem For Semilinear Stochastic Evolution Equations And Stochastic Partial Differential Equations written by Salah-Eldin Mohammed and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations and stochastic partial differential equations near stationary solutions.
Degree Theory For Operators Of Monotone Type And Nonlinear Elliptic Equations With Inequality Constraints
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Author : Sergiu Aizicovici
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Degree Theory For Operators Of Monotone Type And Nonlinear Elliptic Equations With Inequality Constraints written by Sergiu Aizicovici and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
In this paper the authors examine the degree map of multivalued perturbations of nonlinear operators of monotone type and prove that at a local minimizer of the corresponding Euler functional, this degree equals one.
Unitary Invariants In Multivariable Operator Theory
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Author : Gelu Popescu
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-06-05
Unitary Invariants In Multivariable Operator Theory written by Gelu Popescu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-05 with Mathematics categories.
This paper concerns unitary invariants for $n$-tuples $T:=(T_1,\ldots, T_n)$ of (not necessarily commuting) bounded linear operators on Hilbert spaces. The author introduces a notion of joint numerical radius and works out its basic properties. Multivariable versions of Berger's dilation theorem, Berger-Kato-Stampfli mapping theorem, and Schwarz's lemma from complex analysis are obtained. The author studies the joint (spatial) numerical range of $T$ in connection with several unitary invariants for $n$-tuples of operators such as: right joint spectrum, joint numerical radius, euclidean operator radius, and joint spectral radius. He also proves an analogue of Toeplitz-Hausdorff theorem on the convexity of the spatial numerical range of an operator on a Hilbert space, for the joint numerical range of operators in the noncommutative analytic Toeplitz algebra $F_n^\infty$.
Toroidal Dehn Fillings On Hyperbolic 3 Manifolds
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Author : Cameron Gordon
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Toroidal Dehn Fillings On Hyperbolic 3 Manifolds written by Cameron Gordon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The authors determine all hyperbolic $3$-manifolds $M$ admitting two toroidal Dehn fillings at distance $4$ or $5$. They show that if $M$ is a hyperbolic $3$-manifold with a torus boundary component $T 0$, and $r,s$ are two slopes on $T 0$ with $\Delta(r,s) = 4$ or $5$ such that $M(r)$ and $M(s)$ both contain an essential torus, then $M$ is either one of $14$ specific manifolds $M i$, or obtained from $M 1, M 2, M 3$ or $M {14}$ by attaching a solid torus to $\partial M i - T 0$.All the manifolds $M i$ are hyperbolic, and the authors show that only the first three can be embedded into $S3$. As a consequence, this leads to a complete classification of all hyperbolic knots in $S3$ admitting two toroidal surgeries with distance at least $4$.