Degenerate operators on the half-line

On the Half-line

We study uniform error estimates of operational quadrature methods for nonlinear convolution equations on the half-line. Equations of this kind arise in control engineering and diffusion problems. The essential ingredients are the stability of the operational quadrature method in an L setting, which is inherited from the continuous equation by its very construction, and a theorem that says that...

Half-line Schrödinger Operators with No Bound States

We consider Schödinger operators on the half-line, both discrete and continuous, and show that the absence of bound states implies the absence of embedded singular spectrum. More precisely, in the discrete case we prove that if ∆+V has no spectrum outside of the interval [−2, 2], then it has purely absolutely continuous spectrum. In the continuum case we show that if both −∆+V and −∆−V have no ...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Inverse problems for selfadjoint Schrödinger operators on the half line with compactly supported potentials

Inverse problems for selfadjoint Schrödinger operators on the half line with compactly supported potentials Tuncay Aktosun,1,a) Paul Sacks,2,b) and Mehmet Unlu3,c) 1Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76019-0408, USA 2Department of Mathematics, Iowa State University, Ames, Iowa 24061, USA 3Department of Mathematics, Recep Tayyip Erdogan University, 5310...

Inverse Resonance Scattering on the Half Line

For the Schrr odinger operator on the half line we prove the following results: the mapping from real compactly supported potentials to the associated Jost functions (in some class of entire functions) is one-to-one and onto. Moreover, we prove that such potential is uniquely determined by its bound states and resonances.