A Brief Introduction To Berezin Toeplitz Operators On Compact K Hler Manifolds
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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 : 2019-10-16
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 2019-10-16 with 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
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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.--
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.
Toeplitz Operators On K Hler Manifolds
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Author : Tatyana Barron
language : en
Publisher: Springer
Release Date : 2018-07-24
Toeplitz Operators On K Hler Manifolds written by Tatyana Barron and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-24 with Mathematics categories.
The purpose of this Brief is to give a quick practical introduction into the subject of Toeplitz operators on Kähler manifolds, via examples, worked out carefully and in detail. Necessary background is included. Several theorems on asymptotics of Toeplitz operators are reviewed and illustrated by examples, including the case of tori and the 2-dimensional sphere. Applications in the context of multisymplectic and hyperkähler geometry are discussed. The book is suitable for graduate students, advanced undergraduate students, and any researchers.
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.
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.
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.
Holomorphic Morse Inequalities And Bergman Kernels
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Author : Xiaonan Ma
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-14
Holomorphic Morse Inequalities And Bergman Kernels written by Xiaonan Ma and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-14 with Mathematics categories.
This book examines holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel. It opens perspectives on several active areas of research in complex, Kähler and symplectic geometry. A large number of applications are also included, such as an analytic proof of Kodaira's embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, compactification of complete Kähler manifolds of pinched negative curvature, Berezin-Toeplitz quantization, weak Lefschetz theorems, and asymptotics of the Ray-Singer analytic torsion.
Clifford Algebra To Geometric Calculus
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Author : David Hestenes
language : en
Publisher: Springer Science & Business Media
Release Date : 1984
Clifford Algebra To Geometric Calculus written by David Hestenes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.