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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

Abstract

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

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.

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

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

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.
There are 23 citations in total.

Details

Primary Language English
Journal Section Araştırma Makalesi
Authors

Nida Palamut Koşar 0000-0003-2421-7872

Publication Date June 7, 2021
Submission Date February 6, 2021
Acceptance Date April 9, 2021
Published in Issue Year 2021 Volume: 10 Issue: 2

Cite

IEEE N. Palamut Koşar, “On Parseval Identity of q-Sturm-Liouville Problem with Transmission Conditions”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 10, no. 2, pp. 403–414, 2021.

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS