The basis property in $L_{p}$ of the boundary
value problem rationally dependent
on the eigenparameter
Studia Mathematica, Tome 174 (2006) no. 2, pp. 201-212
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
N. B. Kerimov 1 ; Y. N. Aliyev 2
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title = {The basis property in $L_{p}$ of the boundary
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N. B. Kerimov; Y. N. Aliyev. The basis property in $L_{p}$ of the boundary
value problem rationally dependent
on the eigenparameter. Studia Mathematica, Tome 174 (2006) no. 2, pp. 201-212. doi: 10.4064/sm174-2-6
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