A Feynman-Kac formula for Schrodinger 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^+ \in 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.
Feynman integrals with point interactions / E., Franchini; Maioli, Marco. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - STAMPA. - 46:5-6(2003), pp. 685-694. [10.1016/S0898-1221(03)90134-9]
Feynman integrals with point interactions
MAIOLI, Marco
2003
Abstract
A Feynman-Kac formula for Schrodinger 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^+ \in 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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