Convergence of Schrödinger Operators on varying Domains
P. Stollman · Birkhäuser Basel eBooks · 1995
Let H = -Δ + V be a Schrödinger operator on ℝ d , where V = V + - V - is a potential with negative part in the Kato class and positive part in L loc 1 . For any open set G we write H G for the corresponding selfadjoint operator in L 2 (G) which is defined in the following way: denote by ℏ the form associated with H and by ℏ G the closure of ℏ|C C ∞ (G); the associated selfadjoint operator is H G . If V ∈ L loc 2 then H G is just the Friedrichs extension of H | C c ∞ (G).