The basis property in $L_{p}$ of the boundary value problem rationally dependent on the eigenparameter

Volume 174 / 2006

N. B. Kerimov, Y. N. Aliyev Studia Mathematica 174 (2006), 201-212 MSC: 34L10, 34B24, 34L20. DOI: 10.4064/sm174-2-6

Abstract

We consider a Sturm–Liouville operator with boundary conditions rationally dependent on the eigenparameter. We study the basis property in $L_{p}$ of the system of eigenfunctions corresponding to this operator. We determine the explicit form of the biorthogonal system. Using this we establish a theorem on the minimality of the part of the system of eigenfunctions. For the basisness in $L_{2}$ we prove that the system of eigenfunctions is quadratically close to trigonometric systems. For the basisness in $L_{p}$ we use F. Riesz's theorem.

Authors

  • N. B. KerimovInstitute of Mathematics and Mechanics
    National Academy of Sciences
    of Azerbaijan
    F. Agayev St. 9
    Baku AZ 1141, Azerbaijan
    e-mail
  • Y. N. AliyevDepartment of Mathematics
    Faculty of Pedagogics
    Qafqaz University
    Khyrdalan
    Baku AZ 0101, Azerbaijan
    e-mail

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