The basis property in $L_{p}$ of the boundary value problem rationally dependent on the eigenparameter
Volume 174 / 2006
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.
