Separation property for Schrödinger operators in Lp-spaces on non-compact manifolds: An International Journal
Let (M, g) be a manifold of bounded geometry with metric g. We consider a Schrödinger-type differential expression L = ΔM + q, where ΔM is the scalar Laplacian on M and q is a non-negative locally integrable function on M. In the terminology of W.N. Everitt and M. Giertz, the differential expression L is said to be separated in L p(M) if for all u ∈ Lp(M) such that Lu ∈ Lp(M), we have qu ∈ Lp(M). We give sufficient conditions for L to be separated in Lp(M), where 1 < p < ∞. © 2013 Copyright Taylor and Francis Group, LLC.
Complex Variables and Elliptic Equations
Digital Object Identifier (DOI)
Milatovic. (2013). Separation property for Schrödinger operators in L p -spaces on non-compact manifolds: An International Journal. Complex Variables and Elliptic Equations, 58(6), 853–864. https://doi.org/10.1080/17476933.2011.625090