A unified approach to resolvent expansions at thresholds

Results are obtained on resolvent expansions around zero energy for Schrodi nger operators H = -Delta + V(x) on L-2(R-m), where V(x) is a sufficiently rapidly decaying real potential. The emphasis is on a unified approach, val id in all dimensions, which does not require one to distinguish between int egralV(x)dx = 0 and integralV(x)dx not equal 0 in dimensions m = 1, 2. It i s based on a factorization technique and repeated decomposition of the Lipp mann-Schwinger operator. Complete results are given in dimensions m = 1 and m = 2.