4 papers · 1 filter
Metric entropy of the space of holomorphic functions
Siarhei Finski
By Montel's theorem, the continuous functions on a compact subset of a complex manifold that admit uniformly bounded holomorphic extensions to the manifold form a compact set in th…
Kodaira-Iitaka dimension and multiplicity: an analytic perspective
Siarhei Finski
We express the Kodaira-Iitaka dimension and the multiplicity of graded linear series in terms of the intersection theory of the plurisubharmonic envelope associated with the linear…
Geometric quantization on big line bundles
Siarhei Finski
We extend several geometric quantization results to the setting of big line bundles. More precisely, we prove the asymptotic isometry property for the map that associates to a metr…
Bernstein-Markov measures and Toeplitz theory
Siarhei Finski
We prove that Toeplitz operators associated with a Bernstein-Markov measure on a compact complex manifold endowed with a big line bundle form an algebra under composition. As an ap…