Deformation Quantization Of Compact K Hler Manifolds By Berezin Toeplitz Quantization

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Deformation Quantization Of Compact K Hler Manifolds By Berezin Toeplitz Quantization

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Author : Martin Schlichenmaier
language : en
Publisher:
Release Date : 1999

Deformation Quantization Of Compact K Hler Manifolds By Berezin Toeplitz Quantization written by Martin Schlichenmaier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.

Complex Monge Amp Re Equations And Geodesics In The Space Of K Hler Metrics

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Author : Vincent Guedj
language : en
Publisher: Springer
Release Date : 2012-01-05

Complex Monge Amp Re Equations And Geodesics In The Space Of K Hler Metrics written by Vincent Guedj and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-05 with Mathematics categories.

The purpose of these lecture notes is to provide an introduction to the theory of complex Monge–Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (Kähler–Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford–Taylor), Monge–Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi–Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli–Kohn–Nirenberg–Spruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after Phong–Sturm and Berndtsson). Each chapter can be read independently and is based on a series of lectures by R. Berman, Z. Blocki, S. Boucksom, F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, delivered to non-experts. The book is thus addressed to any mathematician with some interest in one of the following fields, complex differential geometry, complex analysis, complex dynamics, fully non-linear PDE's and stochastic analysis.

Deformation Quantization Of Compact K Hler Manifolds Via Berezin Toeplitz Operators

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Author : Martin Schlichenmaier
language : en
Publisher:
Release Date : 1996

Deformation Quantization Of Compact K Hler Manifolds Via Berezin Toeplitz Operators written by Martin Schlichenmaier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.

Spectral Geometry

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Author : Pierre H. Berard
language : en
Publisher: Springer
Release Date : 2006-11-14

Spectral Geometry written by Pierre H. Berard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Jordan Algebras In Analysis Operator Theory And Quantum Mechanics

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Author : Harald Upmeier
language : en
Publisher: American Mathematical Soc.
Release Date : 1987

Jordan Algebras In Analysis Operator Theory And Quantum Mechanics written by Harald Upmeier 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 1987 with Mathematics categories.

Jordan algebras have found interesting applications in seemingly unrelated areas of mathematics such as operator theory, the foundations of quantum mechanics, complex analysis in finite and infinite dimensions, and harmonic analysis on homogeneous spaces. This book describes some relevant results and puts them in a general framework.

Berezin Toeplitz Quantization And Berezin Symbols For Arbitrary Compact K Hler Manifolds

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Author : Martin Schlichenmaier
language : en
Publisher:
Release Date : 1999

Berezin Toeplitz Quantization And Berezin Symbols For Arbitrary Compact K Hler Manifolds written by Martin Schlichenmaier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.

The Spectral Theory Of Toeplitz Operators

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Author : L. Boutet de Monvel
language : en
Publisher: Princeton University Press
Release Date : 1981-08-21

The Spectral Theory Of Toeplitz Operators written by L. Boutet de Monvel and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-08-21 with Mathematics categories.

The theory of Toeplitz operators has come to resemble more and more in recent years the classical theory of pseudodifferential operators. For instance, Toeplitz operators possess a symbolic calculus analogous to the usual symbolic calculus, and by symbolic means one can construct parametrices for Toeplitz operators and create new Toeplitz operators out of old ones by functional operations. If P is a self-adjoint pseudodifferential operator on a compact manifold with an elliptic symbol that is of order greater than zero, then it has a discrete spectrum. Also, it is well known that the asymptotic behavior of its eigenvalues is closely related to the behavior of the bicharacteristic flow generated by its symbol. It is natural to ask if similar results are true for Toeplitz operators. In the course of answering this question, the authors explore in depth the analogies between Toeplitz operators and pseudodifferential operators and show that both can be viewed as the "quantized" objects associated with functions on compact contact manifolds.

Groups And Geometric Analysis

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Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Society
Release Date : 2022-03-17

Groups And Geometric Analysis written by Sigurdur Helgason 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 2022-03-17 with Mathematics categories.

Group-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group. The introductory chapter is a self-contained account of the analysis on surfaces of constant curvature. Later chapters cover general cases of the Radon transform, spherical functions, invariant operators, compact symmetric spaces and other topics. This book, together with its companion volume, Geometric Analysis on Symmetric Spaces (AMS Mathematical Surveys and Monographs series, vol. 39, 1994), has become the standard text for this approach to geometric analysis. Sigurdur Helgason was awarded the Steele Prize for outstanding mathematical exposition for Groups and Geometric Analysis and Differential Geometry, Lie Groups and Symmetric Spaces.

A Brief Introduction To Berezin Toeplitz Operators On Compact K Hler Manifolds

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Author : Yohann Le Floch
language : en
Publisher: Springer
Release Date : 2018-10-02

A Brief Introduction To Berezin Toeplitz Operators On Compact K Hler Manifolds written by Yohann Le Floch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-02 with Mathematics categories.

This text provides a comprehensive introduction to Berezin–Toeplitz operators on compact Kähler manifolds. The heart of the book is devoted to a proof of the main properties of these operators which have been playing a significant role in various areas of mathematics such as complex geometry, topological quantum field theory, integrable systems, and the study of links between symplectic topology and quantum mechanics. The book is carefully designed to supply graduate students with a unique accessibility to the subject. The first part contains a review of relevant material from complex geometry. Examples are presented with explicit detail and computation; prerequisites have been kept to a minimum. Readers are encouraged to enhance their understanding of the material by working through the many straightforward exercises.

A Brief Introduction To Berezin Toeplitz Operators On Compact K Hler Manifolds

DOWNLOAD
Author : Yohann Le Floch
language : en
Publisher:
Release Date : 2018

A Brief Introduction To Berezin Toeplitz Operators On Compact K Hler Manifolds written by Yohann Le Floch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Kählerian manifolds categories.

This text provides a comprehensive introduction to Berezin–Toeplitz operators on compact Kähler manifolds. The heart of the book is devoted to a proof of the main properties of these operators which have been playing a significant role in various areas of mathematics such as complex geometry, topological quantum field theory, integrable systems, and the study of links between symplectic topology and quantum mechanics. The book is carefully designed to supply graduate students with a unique accessibility to the subject. The first part contains a review of relevant material from complex geometry. Examples are presented with explicit detail and computation; prerequisites have been kept to a minimum. Readers are encouraged to enhance their understanding of the material by working through the many straightforward exercises.--