Va. Sadovnichii et Ve. Podolskii, A CLASS OF STURM-LIOUVILLE OPERATORS AND APPROXIMATE CALCULATION OF THE FIRST EIGENVALUES, Sbornik. Mathematics, 189(1-2), 1998, pp. 129-145
A special class S of Sturm-Liouville operators with simple asymptotic
properties of eigenfunctions is investigated. The analytic properties
of the potentials are analyzed and the operators in this class are des
cribed in terms of the transition function of the inverse problem. The
following result is established: the class S is dense in the set of S
turm-Liouville operators with potentials in L-2. A subset of S that al
so has the density property is effectively distinguished. Based on the
properties of the operators in this subset, a method of the approxima
te evaluation of the first eigenvalues of a Sturm-Liouville operator t
hrough its regularized traces is proposed and substantiated.