SAMPLING EIGENVALUES IN HARDY SPACES

摘要

In this work we extend the sampling method to compute eigenvalues of singular non–self-adjoint Sturm–Liouville problems in the presence of a continuous spectrum. We first show that the characteristic function, whose zeros are the eigenvalues, belongs to a Hardy space, and then develop a new sampling formula for its reconstruction. We estimate the truncation error, obtain computable error bounds, and test the method with a few numerical experiments.