On Parseval Identity of q-Sturm-Liouville Problem with Transmission Conditions on Semi Axis

Year 2021, Volume: 10 Issue: 2, 403 - 414, 07.06.2021

Nida Palamut Koşar

https://izlik.org/JA59GZ72AG

Abstract

Makale, transfer koşullu tekil q-Sturm-Liouville problemi için bir spektral fonksiyonun varlığı ile ilgilidir. Ayrıca, özfonksiyonlarda genişleme formülü ve Parseval eşitliği oluşturulmuştur.

Keywords

q-Sturm-Liouville operatörü , , Parseval eşitliği , , spektral fonksiyon , , özfonksiyon genişlemesi

On Parseval Identity of q-Sturm-Liouville Problem with Transmission Conditions

https://izlik.org/JA59GZ72AG

Abstract

References

• Ernst T. 2000. The History of q-calculus and a New Method. Department of Mathematics, Uppsala University, ISSN 1101-3591, 1-230.
• Kac V., Cheung P. 2002. Quantum Calculus. Springer-Verlag, Berlin, 1-118.
• Allahverdiev B.P., Tuna H. 2018. An expansion theorem for q-Sturm-Liouville operators on the whole line. Turkish Journal of Mathematics, 42 (3): 1060-1071.
• Allahverdiev B.P., Tuna H. 2019. Eigenfunction expansion in the singular case for q-Sturm-Liouville operators. Caspian Journal of Mathematical Sciences, 8 (2): 91-102.
• Allahverdiev B.P., Tuna H. 2019. Eigenfunction expansion for singular Sturm-Liouville problems with transmission conditions. Electron J. Differential Equations, 03: 1-10.
• Annaby M.H., Mansour Z.S. 2012. q-Fractional Calculus and Equations. Lecture Notes in Mathematics, Springer-Verlag, Berlin Heidelberg, 1-318.
• Annaby M.H., Mansour Z.S. 2005. Basic Sturm-Liouville problems. J. Phys. A.: Math. Gen., 38 (17): 3775-3797.
• Jackson F.H. 1910. q-difference equations. Am. J. Math., 32 (4): 305-314.
• Jackson F.H. 1910. On q-definite Integrals. Pure Appl. Math.,41 (15): 193-203.
• Levitan B.M., Sagsjan I.S. 1991. Sturm-Liouville and Dirac Operators. Mathematics and its Applications, Kluwer Academic Publishers, London, 1-339.
• Titchmarsh E.C. 1962. Eigenfunction Expansions Associated with Second-Order Differential Equations, Part I. Second Edition Clarendon Press, Oxford, 1-210.
• Annaby M.H., Mansour Z.S. 2011. Asymptotic formulae for eigenvalues and eigenfunctions of q-Sturm-Liouville problems. Math. Nachr., 284 (4): 443-470.
• Annaby M.H., Mansour Z.S., Soliman I.A. 2012. q-Titchmarsh-Weyl theory: series expansion. Nagoya Math. J., 205: 67-118.
• Karahan D., Mamedov Kh.R. 2020. Sampling Theory Associated with q-Sturm-Liouville Operator with Discontinuity Conditions. Journal of Contemporary Applied Mathematics, 10 (2): 40-48.
• Mukhtarov O.Sh., Tunç E. 2004. Eigenvalue problems for Sturm Liouville equations with transmission conditions. Israel J. Math., 144: 367-380.
• Mukhtarov O.Sh., Yakubov S. 2002. Problems for differential equations with transmission conditions. Applicable Anal., 81: 1033-1064.
• Goktas S., Koyunbakan H., Gulsen T. 2018. Inverse nodal problem for polynomial pencil of Sturm‐Liouville operator. Mathematical Methods in the Applied Sciences, 41 (17): 7576-7582.
• Bairamov E., Aygar Y., Oznur B. 2020. Scattering Properties of Eigenparameter Dependent Impulsive Sturm-Liouville Equations. Bulletin of the Malaysian Mathematical Sciences Society, 43: 2769-2781.
• Hahn W. 1949. Beitrage zur Theorie der Heineschen Reiben. Math. Nachr, 2: 340-379 (in German).
• Annaby M.H. 2013. q-Type Sampling Theorems. Results in Mathematics, 44: 214-225.
• Dehghani I., Akbarfam A.J. 2014. Resolvent operator and self-adjointness of Sturm-Liouville operators with a finite number of transmission conditions. Mediterr. J. Math., 11: 447-462.
• Wang A., Sun J., Hao X., Yao S. 2009. Completeness of eigenfunctions of Sturm-Liouville problems with transmission conditions. Math. Appl. Anal., 16: 299-312.
• Kolmogorov A.N., Fomin S.V. 1975. Introductory Real Analysis. Dover Publications, New York, 1-416.