99-413 Bodmann B. G.

A relation of Berezin-Toeplitz operators to Schroedinger operators and the probabilistic representation of Berezin-Toeplitz semigroups (65K, LaTeX) Oct 31, 99

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Abstract. A class of functions is specified 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 Schroedinger operators defined via certain quadratic forms. The probabilistic expression is derived in conjunction with the Feynman-Kac-Ito formula.

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