On the essential spectrum of electromagnetic Schrödinger operator with singular electric potential

Uniform Resolvent Estimates for Magnetic Schrödinger Operators in a 2D Exterior Domain and their Applications to Related Evolution Equations

“…Mochizuki [13]). Moreover, if (1.4) max{|∇ × b(x)|, |c(x)|} = o(r −1 ) as r → ∞ then the essential spectrum of L fills the whole nonnegative half-line [0, ∞) (see Aliev-Eyvazov [1]). The selfadjointness of L shows that its resolvent R(κ 2 ) = (L−κ 2 ) −1 is defined for each κ ∈ Π ± , and u = R(κ 2 )f gives a unique L 2 -solution of the exterior problem (1.1), (1.2).…”