Klein-Gordon operators with complex potentials are formulated as model systems
to examine the possible impact of non-normality on the stellar pulsation eigenvalue
problem. Computations of spectra, ε-pseudospectra and resolvent norms
for these operators
show that extended regions of complex potential, corresponding in stars to non-adiabatic
regions, leads to strong non-normality. Introduction of an advective term further
increases non-normal properties. Prospective model improvements and
implications for resonances and for nonlinear pulsation are considered.