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The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99

2016-03-02 Mathematics
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Release : 2016-03-02
Genre : Mathematics
Kind : eBook
Book Rating : 447/5 ( reviews)

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Book Synopsis The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 by : L. Boutet de Monvel

Download or read book The Spectral Theory of Toeplitz Operators. (AM-99), Volume 99 written by L. Boutet de Monvel. This book was released on 2016-03-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Spectral Theory of Toeplitz Operators

1981 Mathematics
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Release : 1981
Genre : Mathematics
Kind : eBook
Book Rating : 844/5 ( reviews)

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Book Synopsis The Spectral Theory of Toeplitz Operators by : L. Boutet de Monvel

Download or read book The Spectral Theory of Toeplitz Operators written by L. Boutet de Monvel. This book was released on 1981. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds

2018-09-19 Mathematics
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Release : 2018-09-19
Genre : Mathematics
Kind : eBook
Book Rating : 82X/5 ( reviews)

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Book Synopsis A Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds by : Yohann Le Floch

Download or read book A Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds written by Yohann Le Floch. This book was released on 2018-09-19. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysis, Applications, and Computations

2023-12-01 Mathematics
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Release : 2023-12-01
Genre : Mathematics
Kind : eBook
Book Rating : 752/5 ( reviews)

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Book Synopsis Analysis, Applications, and Computations by : Uwe Kähler

Download or read book Analysis, Applications, and Computations written by Uwe Kähler. This book was released on 2023-12-01. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.

The Bergman Kernel and Related Topics

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Genre :
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Book Rating : 06X/5 ( reviews)

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Book Synopsis The Bergman Kernel and Related Topics by : Kengo Hirachi

Download or read book The Bergman Kernel and Related Topics written by Kengo Hirachi. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:

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