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

AbstractA completeness/expansion theorem, analogous to that of DiPrima and Habetler (D-H), 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 Gohberg and Kreǐn