Abstract
A Feynman-Kac formula for Schrödinger operators including a one-center point interaction in R 3 plus a bounded potential is proved. Functional integration methods on similar Kac's averages with point interactions allow us to construct bounded self-adjoint semigroups in L 2( R 3), with bounded below Schrodinger generators, when V + ϵ L loc 2 and V − belongs to a large class of L 2 + L −8 potentials. Moreover, a pointwise bound on the range of the semigroup is given.
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