Asymptotic behavior on (−∞, 0) of the spectral measures of a family of singular Sturm-Liouville operators

Author:

Pechentsov A. S.,Popov A. Yu.

Publisher

Pleiades Publishing Ltd

Subject

General Mathematics,Analysis

Reference6 articles.

1. Weyl, H., Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörige Entwicklungen willkürlicher Functionen, Math. Ann., 1910, vol. 68, pp. 220–268.

2. Titchmarsh, E.C., Eigenfunction Expansions Associated with Second-Order Differential Equations, Oxford: Clarendon, 1958. Translated under the title Razlozheniya po sobstvennym funktsiyam, svyazannye s differentsial’nymi uravneniyami vtorogo poryadka, Moscow: Izdat. Inostr. Lit., 1960.

3. Eastham, M.S.P., The Asymptotic Form of the Spectral Function in Sturm-Liouville Problems with a Large Potential Like −x c (c ≤ 2), Proceedings of the Royal Society of Edinburgh, 1998, vol. 128A, pp. 37–45.

4. Zygmund, A., Trigonometric Series, Cambridge, 1959. Translated under the title Trigonometricheskie ryady, Moscow, 1965.

5. Pechentsov, A.S. and Popov, A.Yu., Spectral Asymptotics of the Sturm-Liouville Operator on the Half-Axis with Potential Tending to −∞. I, II, Differ. Uravn., 2008, vol. 44, no. 5, pp. 640–648; no. 6, pp. 755–767.

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