Kodai Mathematical Journal

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

Bilender P. Allahverdiev

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Abstract

In this study, dissipative singular q-Sturm-Liouville operators are studied in the Hilbert space $\mathcal{L}_{r,q}^{2}$(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.

Article information

Source
Kodai Math. J., Volume 39, Number 1 (2016), 1-15.

Dates
First available in Project Euclid: 22 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1458651688

Digital Object Identifier
doi:10.2996/kmj/1458651688

Mathematical Reviews number (MathSciNet)
MR3478267

Zentralblatt MATH identifier
1350.39003

Citation

Allahverdiev, Bilender P. Spectral problems of non-self-adjoint q -Sturm-Liouville operators in limit-point case. Kodai Math. J. 39 (2016), no. 1, 1--15. doi:10.2996/kmj/1458651688. https://projecteuclid.org/euclid.kmj/1458651688


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