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

Abstract: We obtain eigenvalue enclosures and basisness results for eigen- and associated functions of a non-self-adjoint unbounded linear operator pencil in which 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. [Copyright &y& Elsevier]