A completeness theorem for the linear stability problem of nearly parallel flows (Q1064210)

A completeness/expansion theorem, analogous to that of \textit{R. C. DiPrima} and \textit{G. J. Habetler} [Arch. Ration. Mech. Anal. 34, 218-227 (1969; Zbl 0181.547)], is proved for the equation governing the linear stability of nearly parallel flows, to which the D-H theorem does not apply. It is also proved that only a finite number of eigenvalues with negative real parts can occur. Both results are based on a theorem of \textit{I. C. Gohberg} and \textit{M. G. Krejn} [Introduction to the theory of linear nonselfadjoint operators (1969; Zbl 0181.135)].