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Journals / Fundamental Journal of Mathematics and Applications / 2022 / Cilt: 5 Sayı: 1

Some Spectral Properties of Multiplicative Hermite Equation

Sertaç GÖKTAŞ
Emrah YILMAZ
Ayşe Çiğdem YAR
Pages
32–41
Publication Date
2022-03-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, some spectral properties of the multiplicative Hermite problem are examined in detail.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We reconstruct the Multiplicative Hermite Equation from multiplicative Sturm-Liouville equation.
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Key Findings & Data:A new representation of eigenfunctions for the constructed problem are obtained by the power series solution technique.
💡
Conclusion & Impact:Finally, some spectral properties of the multiplicative Hermite problem are examined in detail.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hermite equation · Multiplicative calculus · Multiplicative Sturm-Liouville equation

Abstract

We reconstruct the Multiplicative Hermite Equation from multiplicative Sturm-Liouville equation. A new representation of eigenfunctions for the constructed problem are obtained by the power series solution technique. While making these solutions, multiplicative Hermite polynomials were used strongly. We get a generator for multiplicative Hermite polynomials and construct integration representations for these polynomials. Finally, some spectral properties of the multiplicative Hermite problem are examined in detail.

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Cite This Article

GÖKTAŞ, S., YILMAZ, E., YAR, A. Ç. (2022). Some Spectral Properties of Multiplicative Hermite Equation. Fundamental Journal of Mathematics and Applications, Cilt: 5 Sayı: 1, 32–41. https://ajindex.com/articles/905677

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References (20)

  1. M. Grossman, An introduction to Non-Newtonian calculus, Int. J. Math. Educ. Sci. Technol., 10(4) (1979) 525-528
  2. M. Grossman, R. Katz, Non-Newtonian Calculus, Lee Press, Pigeon Cove, MA, 1972
  3. A. Benford, The Law of anomalous numbers, Proc. Am. Philos. Soc., 78 (1938) 551-572
  4. A. E. Bashirov, E. M. Kurpınar, A. O¨ zyapıcı, Multiplicative calculus and its applications, J. Math. Anal. Appl., 337 (2008), 36-48
  5. A. E. Bashirov, M. Riza, On complex multiplicative differentiation, TWMS J. Apl. Eng. Math., 1(1) (2011) 75-85
  6. A. E. Bashirov, E. Mısırlı, Y. Tandogdu, A. O¨ zyapıcı, On modeling with multiplicative differential equations, Appl. Math. J. Chinese Univ. Ser. A, 26(4) (2011) 425-438
  7. K. Boruah, B. Hazarika, G-Calculus, TWMS J. Apl. Eng. Math., 8(1) (2018), 94-105
  8. L. Florack, Hv. Assen, Multiplicative calculus in biomedical image analysis, J. Math. Imaging Vis., 42 (2012), 64-75
  9. R. A. Guenther, Product integrals and sum integrals, Int. J. Math. Educ. Sci. Technol., 14(2) (1983), 243-249
  10. A. Slavik, Product Integration, Its History and Applications, Matfyzpress, Prague, 2007
  11. D. Stanley, A multiplicative calculus, Primus, IX (4) (1999), 310-326
  12. S. Goktas, E. Yilmaz, A. C. Yar, Multiplicative derivative and its basic properties on time scales, Math. Methods Appl. Sci., (2021), 310-326,
  13. E. Yilmaz, Multiplicative Bessel equation and its spectral properties, Ric. Mat., (2021), 1-17.
  14. L. C. Andrews, Special Functions of Mathematics for Engineers, SPIE, USA, 1998
  15. X. Duan, Spectral Theory of the Hermite Operator on Lp(Rn), Math. Model. Nat. Phenom., 9 (2014) 39-43
  16. W. N. Everitt, L. L. Littlejohn, R. Wellman, The left-definite spectral theory for the classical Hermite differential equation, J. Comput. Appl. Math., 121 (2000), 313-330
  17. G. Freiling, V. Yurko, Inverse problems for differential operators with singular boundary conditions, Math. Nachr., 278(12-13) (2005) 1561-1578
  18. T. Gulsen, E. Yilmaz, E. S. Panakhov, On a lipschitz stability problem for p-Laplacian Bessel equation, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 66 (2017) 253-262
  19. T. Gulsen, E. Yilmaz, M. Hamadamen, Inverse nodal problem for p-Laplacian Bessel equation with polynomially dependent spectral parameter, Demonstr. Math., 51 (2018) 255-263
  20. E. Hasanov, G. Uzgoren, A. Buyukaksoy, Diferensiyel Denklemler Teorisi, Papat