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math.CV2025
On the Localization of the Bergman Kernel and applications to Toeplitz theory
Siarhei Finski
For a compact complex manifold endowed with a big line bundle and a Radon measure, we study the localization phenomena of the associated Bergman (or Christoffel-Darboux) kernel. Fo…
math.CV2025
Small eigenvalues of Toeplitz operators, Lebesgue envelopes and Mabuchi geometry
Siarhei Finski
We study small eigenvalues of Toeplitz operators on polarized complex projective manifolds. For Toeplitz operators whose symbols are supported on proper subsets, we prove the exist…
math.CV2024
Toeplitz operators, submultiplicative filtrations and weighted Bergman kernels
Siarhei Finski
We demonstrate that the weight operator associated with a submultiplicative filtration on the section ring of a polarized complex projective manifold is a Toeplitz operator. We fur…