Bodmann B. G.
A relation of Berezin-Toeplitz operators to
Schroedinger operators and the probabilistic
representation of Berezin-Toeplitz semigroups
(65K, LaTeX)
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.