Spectral theory of C-symmetric non-selfadjoint differential operators of order 2n

Abstract

We continue the spectral analysis of differential operators with complex coefficients, extending some results for Sturm-Liouville operators to higher order operators. We give conditions for the essential spectrum to be empty, and for the operator to have compact resolvent. Conditions are given on the coefficients for the resolvent to be Hilbert-Schmidt. These conditions are new even for real coefficients, i.e., the selfadjoint case. Asymptotic analysis is a central tool. See also https://ejde.math.txstate.edu/special/02/b2/abstr.html