Author: Alix Deleporte-Dumont
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
Berezin-Toeplitz operators allow to quantize functions, or symbols, on compact Kähler manifolds, and are defined using the Bergman (or Szeg\H{o}) kernel. We study the spectrum of Toeplitz operators in an asymptotic regime which corresponds to a semiclassical limit. This study is motivated by the atypic magnetic behaviour observed in certain crystals at low temperature. We study the concentration of eigenfunctions of Toeplitz operators in cases where subprincipal effects (of same order as the semiclassical parameter) discriminate between different classical configurations, an effect known in physics as quantum selection . We show a general criterion for quantum selection and we give detailed eigenfunction expansions in the Morse and Morse-Bott case, as well as in a degenerate case. We also develop a new framework in order to treat Bergman kernels and Toeplitz operators with real-analytic regularity. We prove that the Bergman kernel admits an expansion with exponentially small error on real-analytic manifolds. We also obtain exponential accuracy in compositions and spectra of operators with analytic symbols, as well as exponential decay of eigenfunctions.
Low-energy Spectrum of Toeplitz Operators
Author: Alix Deleporte-Dumont
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
Berezin-Toeplitz operators allow to quantize functions, or symbols, on compact Kähler manifolds, and are defined using the Bergman (or Szeg\H{o}) kernel. We study the spectrum of Toeplitz operators in an asymptotic regime which corresponds to a semiclassical limit. This study is motivated by the atypic magnetic behaviour observed in certain crystals at low temperature. We study the concentration of eigenfunctions of Toeplitz operators in cases where subprincipal effects (of same order as the semiclassical parameter) discriminate between different classical configurations, an effect known in physics as quantum selection . We show a general criterion for quantum selection and we give detailed eigenfunction expansions in the Morse and Morse-Bott case, as well as in a degenerate case. We also develop a new framework in order to treat Bergman kernels and Toeplitz operators with real-analytic regularity. We prove that the Bergman kernel admits an expansion with exponentially small error on real-analytic manifolds. We also obtain exponential accuracy in compositions and spectra of operators with analytic symbols, as well as exponential decay of eigenfunctions.
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
Berezin-Toeplitz operators allow to quantize functions, or symbols, on compact Kähler manifolds, and are defined using the Bergman (or Szeg\H{o}) kernel. We study the spectrum of Toeplitz operators in an asymptotic regime which corresponds to a semiclassical limit. This study is motivated by the atypic magnetic behaviour observed in certain crystals at low temperature. We study the concentration of eigenfunctions of Toeplitz operators in cases where subprincipal effects (of same order as the semiclassical parameter) discriminate between different classical configurations, an effect known in physics as quantum selection . We show a general criterion for quantum selection and we give detailed eigenfunction expansions in the Morse and Morse-Bott case, as well as in a degenerate case. We also develop a new framework in order to treat Bergman kernels and Toeplitz operators with real-analytic regularity. We prove that the Bergman kernel admits an expansion with exponentially small error on real-analytic manifolds. We also obtain exponential accuracy in compositions and spectra of operators with analytic symbols, as well as exponential decay of eigenfunctions.
Essential Spectrum of Toeplitz Operators on Weighted Bergman Space
Author: Norma Salem Elias
Publisher:
ISBN:
Category : Toeplitz operators
Languages : en
Pages : 84
Book Description
Publisher:
ISBN:
Category : Toeplitz operators
Languages : en
Pages : 84
Book Description
The Spectral Theory of Toeplitz Operators
Author: Anthony Bak
Publisher:
ISBN: 9780691082745
Category : Forms (Mathematics)
Languages : en
Pages : 160
Book Description
Publisher:
ISBN: 9780691082745
Category : Forms (Mathematics)
Languages : en
Pages : 160
Book Description
The Boundedness and Spectral Properties of Multiplicative Toeplitz Operators
Author: Nicola Thorn
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Analysis of Toeplitz Operators
Author: A. Böttcher
Publisher:
ISBN: 9783112707180
Category : Mathematics
Languages : en
Pages : 0
Book Description
No detailed description available for "Analysis of Toeplitz Operators".
Publisher:
ISBN: 9783112707180
Category : Mathematics
Languages : en
Pages : 0
Book Description
No detailed description available for "Analysis of Toeplitz Operators".
Spectral Multiplicity of a Class of Toeplitz Operators with Smooth Symbol
Author: Dmitry V. Jakubovič
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
Book Description
Hyponormal Toeplitz Operators and Weighted Shifts
Author: John Joseph Long
Publisher:
ISBN:
Category : Toeplitz operators
Languages : en
Pages : 118
Book Description
Publisher:
ISBN:
Category : Toeplitz operators
Languages : en
Pages : 118
Book Description
On the Essential Spectra of Toeplitz Operators on Hardy Spaces and the Riemann-Hilbert Problem
Author: Lauren Wolf
Publisher:
ISBN:
Category : Eigenvalues
Languages : en
Pages : 49
Book Description
Publisher:
ISBN:
Category : Eigenvalues
Languages : en
Pages : 49
Book Description
OAR Cumulative Index of Research Results
Author: United States. Air Force. Office of Aerospace Research
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 550
Book Description
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 550
Book Description
Journal of Operator Theory
Author:
Publisher:
ISBN:
Category : Operator theory
Languages : en
Pages : 442
Book Description
Publisher:
ISBN:
Category : Operator theory
Languages : en
Pages : 442
Book Description