Bergman kernel estimates and Toeplitz operators on holomorphic line bundles

2017/07/06 by Asserda, Said
#30H20 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47B35 #Secondary 32A25

paper · doi:10.48550/arxiv.1707.01722

Abstract

We characterize operator-theoretic properties (boundedness, compactness, and Schatten class membership) of Toeplitz operators with positive measure symbols on Bergman spaces of holomorphic hermitian line bundles over Kähler Cartan-Hadamard manifolds in terms of geometric or operator-theoretic properties of measures.

Related

• Upper bounds for Bergman kernels associated to positive line bundles with smooth Hermitian metrics
• Convergence of Bergman measures for high powers of a line bundle
• Bergman kernels and equilibrium measures for line bundles over projective manifolds
• Bergman kernels and equilibrium measures for ample line bundles
• Bernstein-Markov measures and Toeplitz theory