A Transformation Formula Relating Resolvents of Berezin-toeplitz Operators by an Invariance Property of Brownian Motion
نویسنده
چکیده
Using a stochastic representation provided by Wiener-regularized path integrals for the semigroups generated by certain Berezin-Toeplitz operators, a transformation formula for their resolvents is derived. The key property used in the transformation of the stochastic representation is that, up to a time change, Brownian motion is invariant under harmonic morphisms. This result for Berezin-Toeplitz operators is obtained in analogy with a well-known technique generating relations among Schrödinger operators that was recently generalized to Riemannian manifolds [Wittich, J. Math. Phys. 41 (2000), 244].
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