Product formula for imaginary resolvents with application to a modified Feynman integral (Q1081099)

An abstract product formula for imaginary resolvents is proved for a pair of self-adjoint operators A, B of a complex Hilbert space. Here, A is assumed to be nonnegative and the positive part of B is arbitrary while its negative part is small with respect to A in the sense of quadratic forms. The proof is somewhat simpler than the author's original one which required both A and B to be nonnegative. When specialized, this theorem establishes the convergence of the ''modified Feynman integral'' - recently introduced by the author - in the most general case for which the Schrödinger equation can be solved without ambiguity.