Self-adjointness of Schrodinger-type operators with singular potentials on manifolds of bounded geometry
| dc.contributor.author | Milatovic, Ognjen | |
| dc.date.accessioned | 2020-11-25T16:40:49Z | |
| dc.date.available | 2020-11-25T16:40:49Z | |
| dc.date.issued | 2003-06-11 | |
| dc.description.abstract | We 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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 8 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Milatovic, 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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13004 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Schrodinger operator | |
| dc.subject | Self-adjointness | |
| dc.subject | Manifold | |
| dc.subject | Bounded geometry | |
| dc.subject | Singular potential | |
| dc.title | Self-adjointness of Schrodinger-type operators with singular potentials on manifolds of bounded geometry | |
| dc.type | Article |