Feynman integrals with point interactions

A Feynman-Kac formula for Schrodinger operators including a one-center point inter action 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+ is an element of L-loc(2) and V- belongs to a large class of L-2 + L-infinity potentials. Moreover, a pointwise bound on the range of the semigroup is given. (C) 2003 Elsevier Ltd. All rights reserved.