On the basis property of eigenfunctions of a singular second-order differential operator

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• 作者：O. V. Belyantsev (1)
  I. S. Lomov (1)
  
• 刊名：Differential Equations
• 出版年：2012
• 出版时间：August 2012
• 年：2012
• 卷：48
• 期：8
• 页码：1174-1176
• 全文大小：259KB
• 参考文献：1. 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鈥?020.
  2. Il鈥檌n, V.A., / Spektral鈥檔aya teoriya differentsial鈥檔ykh operatorov (Spectral Theory of Differential Operators), Moscow: Nauka, 1991.
  3. 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鈥?134.
  4. Il鈥檌n, 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鈥?053.
  5. Lomov, I.S., Nonsmooth Eigenfunctions in Problems of Mathematical Physics, / Differ. Uravn., 2011, vol. 47, no. 3, pp. 358鈥?65.
  6. Kritskov, L.V., Some Spectral Properties of Singular Ordinary Second-Order Operators, / Cand. Sci. ( / Phys.-Math.) / Dissertation, Moscow, 1990.
  
• 作者单位：O. V. Belyantsev (1)
  I. S. Lomov (1)
  
  1. Moscow State University, Moscow, Russia
  
• ISSN：1608-3083

文摘

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.