Milatovic, Ognjen2020-11-252020-11-252003-06-11Milatovic, O. (2003). Self-adjointness of Schrodinger-type operators with singular potentials on manifolds of bounded geometry. <i>Electronic Journal of Differential Equations, 2003</i>(64), pp. 1-8.1072-6691https://hdl.handle.net/10877/13004We consider the Schrödinger type differential expression HV = ∇*∇ + V, where ∇ is a C∞-bounded Hermitian connection on a Hermitian vector bundle E of bounded geometry over a manifold of bounded geometry (M, g) with metric g and positive C∞-bounded measure dμ, and V = V1 + V2, where 0 ≤ V1 ∈ L1 loc (End E) and 0 ≥ V2 ∈ L1 loc (End E) are linear self-adjoint bundle endomorphisms. We give a sufficient condition for self-adjointness of the operator S in L2(E) defined by Su = HVu for all u ∈ Dom(s) = {u ∈ W1,2(E): ∫⟨V1u, u⟩dμ < +∞ and HVu for all u ∈ L2(E)}. The proof follows the scheme of T. Kato, but it requires the use of more general vision of Kato's inequality for Bochner Laplacian operator as well as a result on the positivity of u ∈ L2(M) satisfying the equation (∆M + b)u = v, where ∆M is the scalar Laplacian on M, b > 0 is a constant and v ≥ 0 is a positive distribution on M.Text8 pages1 file (.pdf)enAttribution 4.0 InternationalSchrodinger operatorSelf-adjointnessManifoldBounded geometrySingular potentialArticle