V. Tkachenko

collaborators

2 papers

math.SP2011

A Schauder and Riesz Basis Criterion for Non-Self-Adjoint Schrödinger Operators with Periodic and Antiperiodic Boundary Conditions

Fritz Gesztesy, Vadim Tkachenko

Under the assumption that $V \in L^{2} ([0, π]; d x)$ , we derive necessary and sufficient conditions for (non-self-adjoint) Schrödinger operators $- d^{2} / d x^{2} + V$ in $L^{2} ([0, π]; d x)$ with…

math.SP2005

When is a non-self-adjoint Hill operator a spectral operator of scalar type?

Fritz Gesztesy, Vadim Tkachenko

We derive necessary and sufficient conditions for a one-dimensional periodic Schrödinger (i.e., Hill) operator H=-d^2/dx^2+V in L^2(R) to be a spectral operator of scalar type. The…