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

N. B. Kerimov ¹   ; Y. N. Aliyev ²

¹ Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan F. Agayev St. 9 Baku AZ 1141, Azerbaijan
² Department of Mathematics Faculty of Pedagogics Qafqaz University Khyrdalan Baku AZ 0101, Azerbaijan

Studia Mathematica, Tome 174 (2006) no. 2, pp. 201-212

Résumé

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.

Détail

DOI : 10.4064/sm174-2-6

Keywords: consider sturm liouville operator boundary conditions rationally dependent eigenparameter study basis property system eigenfunctions corresponding operator determine explicit form biorthogonal system using establish theorem minimality part system eigenfunctions basisness prove system eigenfunctions quadratically close trigonometric systems basisness rieszs theorem