A UNIFIED APPROACH TO RESOLVENT EXPANSIONS AT THRESHOLDS

Abstract

Results are obtained on resolvent expansions around zero energy for Schrödinger operators H=-Δ+V(x) on L2(Rm), where V(x) is a sufficiently rapidly decaying real potential. The emphasis is on a unified approach, valid in all dimensions, which does not require one to distinguish between ∫V(x)dx=0 and ∫V(x)dx≠0 in dimensions m=1,2. It is based on a factorization technique and repeated decomposition of the Lippmann–Schwinger operator. Complete results are given in dimensions m=1 and m=2.