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Journals / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 6

q−Hamiltonian systems

Bilender PAŞAOĞLU ALLAHVERDİEV
Hüseyin TUNA
Pages
2241–2258
Publication Date
2022-11-01
DOI
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Finally, we give a spectral resolution.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we develop the basic theory of linear q− Hamiltonian systems.
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Key Findings & Data:In this context, we establish an existence and uniqueness result.
💡
Conclusion & Impact:Finally, we give a spectral resolution.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we develop the basic theory of linear q− Hamiltonian systems. In this context, we establish an existence and uniqueness result. Regular spectral problems are studied. Later, we introduce the corresponding maximal and minimal operators for this system. Finally, we give a spectral resolution.

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Cite This Article

ALLAHVERDİEV, B. P., TUNA, H. (2022). q−Hamiltonian systems. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 6, 2241–2258. https://ajindex.com/articles/607537

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References (17)

  1. Abu-Risha MH, Annaby MH, Ismail MEH, Mansour ZS. Linear q−difference equations. Zeitschrift fur Analysis und ihre Anwendungen 2007; 26: 481-494
  2. Ahlbrandt CD, Peterson AC. Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Ricatti Equations. Boston, MA, USA: Kluwer Academic Publishers Group, 1996
  3. Allahverdiev BP, Tuna H. An expansion theorem for q−Sturm-Liouville operators on the whole line. Turkish Journal of Mathematics 2018; 42: 1060-1071
  4. Allahverdiev BP, Tuna H. Limit-point criteria for q−Sturm-Liouville equations. Quaestiones Mathematicae 2019; 42 (10): 1291-1299
  5. Allahverdiev BP, Tuna H. One-dimensional q−Dirac equation. Mathematical Methods in the Applied Sciences 2017; 40: 7287-7306
  6. Allahverdiev BP, Tuna H. Dissipative q−Dirac operator with general boundary conditions. Quaestiones Mathematicae 2018; 41 (2): 239-255
  7. Allahverdiev BP, Tuna H. On expansion in eigenfunction for q−Dirac systems on the whole line. Mathematical Reports 2019; 21 (3): 369-382
  8. Allahverdiev BP, Tuna H. Titchmarsh-Weyl theory for q−Dirac systems. Infinite Dimensional Analysis, Quantum Probability and Related Topics 2019; 22 (2): 1950010
  9. Allahverdiev BP, Tuna H. Properties of the resolvent of singular q−Dirac operators. Electronic Journal of Differential Equations 2020; 2020 (3): 1-13
  10. Allahverdiev BP, Tuna H. Qualitative spectral analysis of singular q−Sturm-Liouville operators. Bulletin of the Malaysian Mathematical Sciences Society 2020; 43: 1391
  11. Allahverdiev BP, Tuna H. Eigenfunction expansion in the singular case for q−Sturm-Liouville operators. Caspian Journal of Mathematical Sciences 2019; 8 (2): 91-102
  12. Anderson DR. Titchmarsh–Sims–Weyl theory for complex Hamiltonian systems on Sturmian time scales. Journal of Mathematical Analysis and Applications 2011; 373: 709-725
  13. Annaby MH, Mansour ZS. Basic Sturm–Liouville problems. Journal of Physics A: Mathematical and Theoretical 2005; 38: 3775-3797
  14. Annaby MH, Hassan HA, Mansour ZS. Sampling theorems associated with singular q−Sturm Liouville problems. Results in Mathematics 2012; 62: 121-136
  15. Annaby MH, Mansour ZS. q−Fractional Calculus and Equations. In: Lecture Notes in Mathematics, Vol. 2056. Heidelberg, Germany: Springer-Verlag, 2012
  16. Atkinson FV. Discrete and Continuous Boundary Problems. New York, NY, USA: Academic Press Inc., 1964
  17. Bangerezako G. q−Difference linear control systems. Journal of Difference Equation