Research Articles

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Forward scattering on the line with a transfer condition.
(Springer International Publishing, 2013-12) Currie, S.; Nowaczyk, M.; Watson, B.A.
We consider scattering on the line with a transfer condition at the origin. Under suitable growth conditions on the potential, the spectrum consists of a finite number of eigenvalues which are negative real numbers, while the remainder is continuous spectrum which is comprised of the positive real axis. Asymptotics are provided for the Jost solutions. Conditions which characterize transfer conditions resulting in self-adjoint problems are found. Properties are given of the scattering coefficient linking it to the spectrum.
Self-adjoint higher order differential operators with eigenvalue parameter dependent boundary conditions.
(Springer International Publishing, 2015-12) Möller, M.; Zinsou, B.
Eigenvalue problems for even order regular quasi-differential equations with boundary conditions which depend linearly on the eigenvalue parameter λ can be represented by an operator polynomial (Formula presented.) where M is a self-adjoint operator. Necessary and sufficient conditions are given such that also K and A are self-adjoint.