On a Domain Characterization of Schrodinger Operators with Gradient Magnetic Vector Potentials and Singular Potentials

Jerome A. Goldstein, Roman Svirsky
1989 Proceedings of the American Mathematical Society  
Of concern are the minimal and maximal operators on L2(R") associated with the differential expression Te = J2{id/dxJ + qJ{x))2 + W{x) j=i where (q.#") = gradQ for some real function W on R" and W satisfies ¿M-2 < W(Jf) < C|x|~2 . In particular, for Q = 0, Xq reduces to the singular Schrödinger operator -A+ W{x). Among other results, it is shown that the maximal operator (associated with the xq ) is the closure of the minimal operator, and its domain is precisely Dom [ ^2(id/dXj + qj(x))1 J n Dom(tt'),
doi:10.2307/2046944 fatcat:5v3bwdcfmfhpjpgphj4pp256pe