Resolvent Asymptotics Near a Two-Cluster Threshold

This chapter is devoted to the asymptotics of the resolvent near an arbitrary two-cluster threshold \(\lambda _0\) of the generalized N-body Schrödinger operator H. As discussed in Chap. 5 , the effective potential for physical models may decay like \(\mathcal {O}(|{x_a}|^{-1})\) (slowly decaying case), \(\mathcal {O}(|{x_a}|^{-2})\) (critically decaying case) or \(\mathcal {O}(|{x_a}|^{-3})\) (very short-range case).