Correction to “The Wiener integral and the Schrödinger operator”

Abstract

This is a correction of a technical nature to the paper mentioned in the title and hereafter referred to as [0]. Other bibliographic references with the exception of [0] will be the bibliographic references given in [0]. We shall use the notation and results given there through Lemma 2 without further comment. The error in [0] first appears in the proof of Lemma 3, and affects that part of the proof of Theorem 1 which appears after Lemma 3. Similar difficulties arise in the proof of Theorem 2, but since the proof is essentially the same, we only make a few brief remarks concerning it. The revisions of the theorem that must be made are sufficiently mild that they do not affect the applicability of the results the (formal) Schrodinger differential operators which arise in physics. Before stating the revised version of Theorem 1 we make the following DEFINITION. A vector field b on R is said to be an admissible vector potential if it is of class C2 and f I b I2exp[ al x 12]dx 0. An extended real-valued Borel measurable function V on R is said to be a b-amissible scalar potential if in the notation of [0] we have: (i) D(V+) n D(X(b; 0; CO) is dense in L2(RN); and (ii) D(V-) c CO and there exists k > oo such that for all 0 e C (R) we have