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Toeplitz operators, submultiplicative filtrations and weighted Bergman kernels
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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 further analyze the asymptotics of the associated weighted Bergman kernel, presenting the local refinement of earlier results on the convergence of jumping measures for submultiplicative filtrations towards the pushforward measure defined by the corresponding geodesic ray.
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Bernstein-Markov measures and Toeplitz theory
For Bernstein-Markov measures on big line bundles, Bergman measures concentrate on the diagonal and Toeplitz operators close under composition, with spectra governed by the equilibrium measure.
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