Semiclassical spectral estimates for Toeplitz operators

David Borthwick; Thierry Paul; Alejandro Uribe

Annales de l'institut Fourier (1998)

  • Volume: 48, Issue: 4, page 1189-1229
  • ISSN: 0373-0956

Abstract

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Let X be a compact Kähler manifold with integral Kähler class and L → X a holomorphic Hermitian line bundle whose curvature is the symplectic form of X . Let H ∈ C ∞ ( X , ℝ ) be a Hamiltonian, and let T k be the Toeplitz operator with multiplier H acting on the space ℋ k = H 0 ( X , L ⊗ k ) . We obtain estimates on the eigenvalues and eigensections of T k as k → ∞ , in terms of the classical Hamilton flow of H . We study in some detail the case when X is an integral coadjoint orbit of a Lie group.

How to cite

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Borthwick, David, Paul, Thierry, and Uribe, Alejandro. "Semiclassical spectral estimates for Toeplitz operators." Annales de l'institut Fourier 48.4 (1998): 1189-1229. <http://eudml.org/doc/75314>.

@article{Borthwick1998,
abstract = {Let $X$ be a compact Kähler manifold with integral Kähler class and $L\rightarrow X$ a holomorphic Hermitian line bundle whose curvature is the symplectic form of $X$. Let $H\in C^\infty (X,\{\Bbb R\})$ be a Hamiltonian, and let $T_k$ be the Toeplitz operator with multiplier $H$ acting on the space $\{\cal H\}_k = H^0(X, L^\{\otimes k\})$. We obtain estimates on the eigenvalues and eigensections of $T_k$ as $k\rightarrow \infty $, in terms of the classical Hamilton flow of $H$. We study in some detail the case when $X$ is an integral coadjoint orbit of a Lie group.},
author = {Borthwick, David, Paul, Thierry, Uribe, Alejandro},
journal = {Annales de l'institut Fourier},
keywords = {Toeplitz operators; semiclassical analysis; spectral theory; geometric quantization},
language = {eng},
number = {4},
pages = {1189-1229},
publisher = {Association des Annales de l'Institut Fourier},
title = {Semiclassical spectral estimates for Toeplitz operators},
url = {http://eudml.org/doc/75314},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Borthwick, David
AU - Paul, Thierry
AU - Uribe, Alejandro
TI - Semiclassical spectral estimates for Toeplitz operators
JO - Annales de l'institut Fourier
PY - 1998
PB - Association des Annales de l'Institut Fourier
VL - 48
IS - 4
SP - 1189
EP - 1229
AB - Let $X$ be a compact Kähler manifold with integral Kähler class and $L\rightarrow X$ a holomorphic Hermitian line bundle whose curvature is the symplectic form of $X$. Let $H\in C^\infty (X,{\Bbb R})$ be a Hamiltonian, and let $T_k$ be the Toeplitz operator with multiplier $H$ acting on the space ${\cal H}_k = H^0(X, L^{\otimes k})$. We obtain estimates on the eigenvalues and eigensections of $T_k$ as $k\rightarrow \infty $, in terms of the classical Hamilton flow of $H$. We study in some detail the case when $X$ is an integral coadjoint orbit of a Lie group.
LA - eng
KW - Toeplitz operators; semiclassical analysis; spectral theory; geometric quantization
UR - http://eudml.org/doc/75314
ER -

References

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