Non‐Self‐Adjoint Differential Operators

A description is given of methods that have been used to analyze the spectrum of non‐self‐adjoint differential operators, emphasizing the differences from the self‐adjoint theory. It transpires that even in cases in which the eigenfunctions can be determined explicitly, they often do not form a basis; this is closely related to a high degree of instability of the eigenvalues under small perturbations of the operator. 2000 Mathematics Subject Classification 34L05, 35P05, 47A10, 47A12.