Singular non-selfadjoint differential operators

Abstract

A characterisation is obtained of all the regularly solvable operators and their adjoints generated by general ordinary quasidifferential expressions inThe domains of these operators are described in terms of boundary conditions involving thesolutions ofM[u] =λwuand the adjoint equationat both singular end-pointsaandb.These results are an extension of those proved in [3], by Evans and Ibrahim, to the case of two singular end-points of the interval (a, b), and a generalisation of those in [10] and [13] concerning selfadjoint andJ-selfadjoint differential operators, whereJdenotes complex conjugation.