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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.

MSC:
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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