Spectral inclusion and spectral exactness for singular non-self-adjoint Sturm-Liouville problems

B.M Brown , M Marletta

Abstract

We consider the effect of regularization by interval truncation on the spectrum of a singular non‐self‐adjoint Sturm‐Liouville operator. We present results on spectral inclusion and spectral exactness for the cases where the singularity is in Sims case II or Sims case III. For Sims case I, we present a test for spectral inexactness, which can be used to detect when the interval truncation process is generating spurious eigenvalues. Numerical results illustrate the effectiveness of this test.