Spectral bounds and basis results for non-self-adjoint pencils, with an application to Hagen–Poiseuille flow

We obtain eigenvalue enclosures and basisness results for eigen- and associated functions of a non-self-adjoint unbounded linear operator pencil A−λB in which B is uniformly positive and the essential spectrum of the pencil is empty. Both Riesz basisness and Bari basisness results are obtained. The results are applied to a system of singular differential equations arising in the study of Hagen–Poiseuille flow with non-axisymmetric disturbances.