On Convergence of Toeplitz Quantization of the Sphere

Yanlin Li (), Mohamed Lemine H. Bouleryah and Akram Ali
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Yanlin Li: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Mohamed Lemine H. Bouleryah: Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
Akram Ali: Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia

Mathematics, 2024, vol. 12, issue 22, 1-15

Abstract: In this paper, we give an explicit expression of the Toeplitz quantization of a C ∞ smooth function on the sphere and show that the sequence of spectra of Toeplitz quantization of the function determines its decreasing rearrangement. We also use Toeplitz quantization to prove a version of Szegö’s Theorem.

Keywords: complex line bundle; symplectic geometry; Toeplitz quantization; decreasing rearrangement; spectral measure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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