On the basis property of eigenfunctions of a singular second-order differential operator
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
We consider the first boundary value problem for a singular differential operator of second order on an interval with transmission conditions at an interior point of the interval. We show that the system of eigenfunctions corresponding to this problem is complete in the space L 2(0, 1) and forms a Riesz basis in that space.
- Belyantsev, O.V., The Bessel Inequality and the Basis Property of Root Functions of a Second-Order Singular Differential Operator, Differ. Uravn., 2000, vol. 36, no. 2, pp. 1011–1020.
- Il’in, V.A., Spektral’naya teoriya differentsial’nykh operatorov (Spectral Theory of Differential Operators), Moscow: Nauka, 1991.
- Zhornitskaya, L.A. and Serov, V.S., A Uniqueness Theorem for the Sturm-Liouville Operator on a Segment with a Potential That Has a Nonintegrable Singularity, Differ. Uravn., 1993, vol. 29, no. 12, pp. 2125–2134.
- Il’in, V.A., Unconditional Basis Property on a Closed Interval of Systems of Eigen- and Associated Functions of a Second-Order Differential Operator, Dokl. Akad. Nauk SSSR, 1983, vol. 273, no. 5, pp. 1048–1053.
- Lomov, I.S., Nonsmooth Eigenfunctions in Problems of Mathematical Physics, Differ. Uravn., 2011, vol. 47, no. 3, pp. 358–365.
- Kritskov, L.V., Some Spectral Properties of Singular Ordinary Second-Order Operators, Cand. Sci. (Phys.-Math.) Dissertation, Moscow, 1990.
- On the basis property of eigenfunctions of a singular second-order differential operator
Volume 48, Issue 8 , pp 1174-1176
- Cover Date
- Print ISSN
- Online ISSN
- SP MAIK Nauka/Interperiodica
- Additional Links