On the number of negative eigenvalues of Schrödinger operators with an Aharonov–Bohm magnetic field

Abstract

It is proved that for V+=max(V,0) in the subspace L1(R+ ; L∞(S1); r dr) of L1(R2), there is a Cwikel–Lieb–Rosenblum–type inequality for the number of negative eigen2 R values of the operator ((1/i)∇ + A)2 — V in L2(R2) when A is an Aharonov-Bohm magnetic potential with non-integer flux. It is shown that the L1(R+, L∞ (S1),r dr)-norm cannot be replaced by the L1(R2)-norm in the inequality.