Spectral inclusion and spectral exactness for singular non-self-adjoint Sturm-Liouville problems. (English) Zbl 0992.34017

The authors consider singular nonselfadjoint Sturm-Liouville operators regularized by truncation of the interval. They develop conditions under which the spectra of a sequence of regularized problems can (a) provide approximations to the whole spectrum of the original singular eigenvalue problem (spectral inclusion) and (b) not yield approximations to any points which are not in the spectrum of the original singular problem (spectral exactness). In the case when the conditions above are violated the authors propose conditions for pseudo-spectral inclusion and pseudo-spectral exactness.


34B24 Sturm-Liouville theory
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators


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