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Distribution of eigenvalues and trace formula for the Sturm-Liouville operator equation. (Russian, English) Zbl 1224.34278
Ukr. Mat. Zh. 62, No. 7, 867-877 (2010); translation in Ukr. Math. J. 62, No. 7, 1005-1017 (2010).
Summary: We study the asymptotic distribution of eigenvalues of the problem generated by the Sturm-Liouville operator equation. A formula for the regularized trace of the corresponding operator is obtained.

34L05 General spectral theory of ordinary differential operators
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
34B24 Sturm-Liouville theory
47E05 General theory of ordinary differential operators (should also be assigned at least one other classification number in Section 47-XX)
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