A Relation of Berezin-toeplitz Operators to Schrr Odinger Operators and the Probabilistic Representation of Berezin-toeplitz Semigroups
نویسنده
چکیده
A class of functions is speciied which give rise to semibounded quadratic forms on weighted Bergman spaces and thus can be interpreted as symbols of self-adjoint Berezin-Toeplitz operators. A similar class admits a probabilistic expression of the sesqui-analytic integral kernel for the associated semigroups. Both results are the consequence of a relation of Berezin-Toeplitz operators to Schrr odinger operators deened via certain quadratic forms. The probabilistic expression is derived in conjunction with the Feynman-Kac-It^ o formula.
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