Some spectral problems of a diffusion operator under Paley-Wiener-based high-order approximations
Main Article Content
Abstract
In this study, we acquired spectral results for the diffusion operator under higher-order approximations. We reconstruct the well-known techniques and derive the essential results for the presented problem. The spectral results for the diffusion operator with high-order approximations were evaluated, focusing on solutions in the Paley-Wiener space. Additionally, we consider theorems that involve solutions belonging to the Paley-Wiener space and the applications of Shannon's sampling theorem. We also examine and evaluate the diffusion operator under more general separable boundary conditions.
Downloads
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
- Authors keep the rights and guarantee the Journal of Innovative Applied Mathematics and Computational Sciences the right to be the first publication of the document, licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License that allows others to share the work with an acknowledgement of authorship and publication in the journal.
- Authors are allowed and encouraged to spread their work through electronic means using personal or institutional websites (institutional open archives, personal websites or professional and academic networks profiles) once the text has been published.
References
[1] M. Babaoglu and E. S. Panakhov, On Some Spectral Problems for Diffusion Operator, ITM Web of Conferences, 13(01036) (2017). DOI: 10.1051/itmconf/20171301036
[2] E. Bairamov, Ö. Çakar and A. O. Çelebi, Quadratic pencil of Schrödinger operators with spectral singularities: Discrete spectrum and principal functions, Journal of Mathematical Analysis and Applications, 216(1) (1997), 303–320. DOI: 10.1006/jmaa.1997.5689
[3] A. Boumenir and B. Chanane, Eigenvalues of Sturm-Liouville systems using sampling theory, Applicable Analysis, 62(3-4) (1996), 323–334. DOI: 10.1080/00036819608840486
[4] A. Boumenir and B. Chanane, Computing eigenvalues of Sturm-Liouville systems of Bessel type, Proceedings of the Edinburgh Mathematical Society, 42(2) (1999), 257–265. DOI: 10.1017/S001309150002023X
[5] K. Chadan and P.C. Sabatier, Inverse Problems in Quantum Scattering Theory, Second edition, Springer-Verlag, 1989.
[6] B. Chanane, High Order Approximations of the Eigenvalues of Regular Sturm-Liouville Problems, Journal of Mathematical Analysis and Applications, 226(1) (1998), 121–129. DOI: 10.1006/jmaa.1998.6049
[7] B. Chanane, Computing eigenvalues of regular Sturm-Liouville problems, Applied Mathematics Letters, 12(7) (1999), 119–125. DOI: 10.1016/S0893-9659(99)00111-1
[8] B. Chanane, Computing the eigenvalues of singular Sturm-Liouville problems using the regularized sampling method, Applied Mathematics and Computation, 184(2) (2007), 972–978. DOI: 10.1016/j.amc.2006.05.187
[9] B. Chanane, Sturm-Liouville problems with parameter dependent potential and boundary conditions, Journal of Computational and Applied Mathematics, 212(2) (2008), 282–290. DOI: 10.1016/j.cam.2006.12.006
[10] M. G. Gasymov and G. Sh. Guseinov, Determination of a diffusion operator from spectral data, Dokl. Akad. Nauk Azerb. SSR, 37(2) (1981), 19–23.
[11] H. Koyunbakan and E. S. Panakhov, Half-inverse problem for diffusion operators on the finite interval, Journal of Mathematical Analysis and Applications, 326(2) (2007), 1024–1030. DOI: 10.1016/j.jmaa.2006.03.068
[12] B. M. Levitan and I. S. Sargsjan, Introduction to Spectral Theory: Selfadjoint Ordinary Differential Operators, American Mathematical Society, Providence, Rhode Island, 1975.
[13] M. A. Naimark, Linear Differential Operators, Part II, New York, 1968.
[14] E. S. Panakhov and M. Babaoglu, Spectral Problems for Regular Canonical Dirac Systems, Proceedings of the Institute of Applied Mathematics, 5(2) (2016), 175–183. URL
[15] A. I. Zayed, Advances in Shannon’s Sampling Theory, CRC Press, Boca Raton, 1993.