Spectral problems of non-self-adjoint q-Sturm-Liouville operators in limit-point case

Kodai Mathematical Journal

Bilender P. Allahverdiev¹ 

[1] Department of Mathematics Suleyman Demirel University

关键词: q-Sturm-Liouville equations;    dissipative operators;    self-adjoint dilation;    scattering function;    characteristic function;    completeness of the root functions;   

DOI  :  10.2996/kmj/1458651688

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(18)In this study, dissipative singular q-Sturm-Liouville operators are studied in the Hilbert space $\mathcal{L}$2r,q(Rq,+), that the extensions of a minimal symmetric operator in limit-point case. We construct a self-adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax-Phillips. Then, we create a functional model of the maximal dissipative operator via the incoming spectral representation and define its characteristic function in terms of the Weyl-Titchmarsh function (or scattering function of the dilation) of a self-adjoint q-Sturm-Liouville operator. Finally, we prove the theorem on completeness of the system of eigenfunctions and associated functions (or root functions) of the dissipative q-Sturm-Liouville operator.

【 授权许可】

Unknown