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Journals / Turkish Journal of Mathematics / 2018 / Cilt: 42 - Sayı: 3

An expansion theorem for q -Sturm–Liouville operators on the whole line

Bilender PAŞAOĞLU ALLAHVERDIEV
Hüseyin TUNA
Pages
1060–1071
Publication Date
2022-11-04
DOI
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⚡ TL;DR(Too Long; Didn't Read)

In this work, we establish a Parseval equality and an expansion formula in eigenfunctions for a singularq−Sturm-Liouville operator on the whole line.

📌 3 Key Takeaways

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Objective & Hypothesis:In this work, we establish a Parseval equality and an expansion formula in eigenfunctions for a singularq−Sturm-Liouville operator on the whole line.
📊
Key Findings & Data:In this work, we establish a Parseval equality and an expansion formula in eigenfunctions for a singularq−Sturm-Liouville operator on the whole line.
💡
Conclusion & Impact:In this work, we establish a Parseval equality and an expansion formula in eigenfunctions for a singularq−Sturm-Liouville operator on the whole line.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this work, we establish a Parseval equality and an expansion formula in eigenfunctions for a singularq−Sturm-Liouville operator on the whole line.

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Cite This Article

ALLAHVERDIEV, B. P., TUNA, H. (2022). An expansion theorem for q -Sturm–Liouville operators on the whole line. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 3, 1060–1071. https://ajindex.com/articles/607887

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References (14)

  1. Annaby MH, Mansour ZS. q -Fractional Calculus and Equations. Lecture Notes in Mathematics, Vol 2056. Heidelberg, Germany: Springer-Verlag, 2012
  2. Annaby MH, Mansour ZS, Soliman IA. q -Titchmarsh-Weyl theory: series expansion. Nagoya Math J 2012; 205: 67-118
  3. Ernst T. The History of q -Calculus and a New Method. U. U. D. M. Report. Uppsala, Sweden: Department of Mathematics of Uppsala University, 2000
  4. Euler L. Introductio in Analysin Infinitorum, Vol
  5. Lausanne, Switzerland: Bousquet, 1748 (in Latin)
  6. Guseinov GS. Eigenfunction expansions for a Sturm-Liouville problem on time scales. Int J Difference Equ 2007; 2: 93-104
  7. Guseinov GS. An expansion theorem for a Sturm-Liouville operator on semi-unbounded time scales. Adv Dyn Syst Appl 2008; 3: 147-160
  8. Hahn W. Beitr¨age zur Theorie der Heineschen Reihen. Math Nachr 1949; 2: 340-379 (in German)
  9. Jackson FH. On q -definite integrals. Quart J Pure Appl Math 1910; 41: 193-203
  10. Kac V, Cheung P. Quantum Calculus. New York, NY, USA: Springer-Verlag, 2002
  11. Kolmogorov AN, Fomin SV, Introductory Real Analysis. Translated by R.A. Silverman. New York, NY, USA: Dover Publications, 1970
  12. Levitan BM, Sargsjan IS. Sturm-Liouville and Dirac Operators. Mathematics and its Applications (Soviet Series). Dordrecht, the Netherlands: Kluwer Academic Publishers Group, 1991
  13. Swamy PN. Deformed Heisenberg algebra: origin of q -calculus. Physica A 2003; 328: 1-2. 145–153
  14. Titchmarsh EC. Eigenfunction Expansions Associated with Second-Order Differential Equations. Part I. 2nd ed. Oxford, UK: Clarendon Press, 1962.