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Mathematics > Spectral Theory

arXiv:1801.00366 (math)
[Submitted on 31 Dec 2017]

Title:Szegö Limit Theorems for Singular Berezin-Toeplitz Operators

Authors:Salvador Pérez-Esteva, Alejandro Uribe
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Abstract:We consider Berezin-Toeplitz operators whose multipliers are compactly supported densities carried by a submanifold of ${\mathbb C}^N$ . We compute asymptotically the moments of their spectral measures, and we prove Szegö limit theorems in cases when the submanifold is isotropic or co-isotropic, from which Weyl estimates follow. We also obtain asymptotics of the Schatten norms of such operators. Rescaled versions of these operators can be thought of as quantum mechanical mixed states, and our results give the semi-classical limit of their entropy.
Comments: 33 pages, 2 figures
Subjects: Spectral Theory (math.SP)
MSC classes: 47B35 (primary), 81Q20 (secondary)
Cite as: arXiv:1801.00366 [math.SP]
  (or arXiv:1801.00366v1 [math.SP] for this version)
  https://doi.org/10.48550/arXiv.1801.00366

Submission history

From: Alejandro Uribe [view email]
[v1] Sun, 31 Dec 2017 22:23:11 UTC (44 KB)
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