Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2020 / Cilt: 10 - Sayı: 1

Inverse Spectral Problems for Second Order Difference Equations with Generalized Function Potentials by aid of Parseval Formula

Parseval Formülü yardımıyla Genelleşmiş Fonksiyon Katsayılı İkinci Mertebeden Fark Denklemleri için Ters Spektral Problemler

Pages
226–239
Publication Date
2022-10-12
DOI
—
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AI Summary & Key Takeaways

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

Keywords: Parseval formula; Spectral analysis; Two spectra.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present study we are investigated inverse spectral problems for spectral analysis and two spectra of matrix by using equality which is equivalance Parseval formula.
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Key Findings & Data:The matrix is tridiagonal almost-symmetric matrix.
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Conclusion & Impact:Keywords: Parseval formula; Spectral analysis; Two spectra.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In the present study we are investigated inverse spectral problems for spectral analysis and two spectra of matrix by using equality which is equivalance Parseval formula. The matrix is tridiagonal almost-symmetric matrix. The mean of almost-symmetric is the entries above and below the main diagonal are the same except the entries and . Keywords: Parseval formula; Spectral analysis; Two spectra.

Özet

Bu çalışmada, Parseval formülü ile eşdeğer olan eşitlik kullanılarak matrisinin spektral analizine göre ve iki spektrumuna göre ters spektral problemleri incelenmiştir. , tipinde hemen hemen simetrik üçköşegensel matristir. Hemen hemen simetriklik, ve elemanları dışında matrisin köşegeninin altında ve üstündeki elemanları eşit olmasıdır. Anahtar Kelimeler: Parseval formülü; Spektral analiz; İki spektrum.

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Cite This Article

BALA, B. (2022). Inverse Spectral Problems for Second Order Difference Equations with Generalized Function Potentials by aid of Parseval Formula. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 10 - Sayı: 1, 226–239. https://ajindex.com/articles/428430

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References (15)

  1. Hochstadt, H., On some inverse problems in matrix theory, Archiv der Mathematik, 18(2), 201-207, 1967.
  2. Hochstadt, H., On the construction of a Jacobi matrix from spectral data, Linear Algebra and Its Applications, 8(5), 435-446, 1974.
  3. Hochstadt, H., On the construction of a Jacobi matrix from mixed given data, Linear Algebra and its Applications, 28, 113-115, 1979.
  4. Fu, L., Hochstadt, H., Inverse theorems for Jacobi matrices, Journal of Mathematical Analysis and Applications, 47(1), 162-168, 1974.
  5. Gasymov, M.G., Guseinov, G.Sh., On inverse problems of spectral analysis for infinite Jacobi matrices in the limit-circle case, In Soviet Mathematics Doklady, 40, 627-630, 1990.
  6. Guseinov, G.Sh., Determination of an infinite non-selfadjoint Jacobi matrix from its generalized spectral function, Matematicheskie Zametki, 23, 237-248, 1978; English transl.: Mathematical Notes, 23, 130-136, 1978.
  7. Guseinov, G.Sh., The inverse problem from the generalized spectral matrix for a second order non-selfadjoint difference equation on the axis, Izvetsiya Akademii Nauk Azerb. SSR Ser. Fiz.-Tekhn. Mat. Nauk, 5, 16-22, 1978 (in Russian) Guseinov, G.Sh., An inverse spectral problem for complex Jacobi matrices, Communications in Nonlinear Science and Numerical Simulation, 15(4), 840-851, 2010.
  8. Guseinov, G.Sh., Construction of a complex Jacobi matrix from two-spectra, Hacettepe Journal of Mathematics and Statistics, 40(2), 2011.
  9. Guseinov, G. Sh., On construction of a complex finite Jacobi matrix from two-spectra, Electronic Journal of Linear Algebra, 26, 101-120, 2013.
  10. Guseinov, G.Sh., On a discrete inverse problem for two spectra, Discrete Dynamics in Nature and Society, 14 pages, 2012.
  11. Guseinov, G.Sh., On an inverse problem for two spectra of finite Jacobi matrices, Applied Mathematics and Computation, 218(14), 7573-7589, 2012.
  12. Guseinov, G.Sh., Inverse spectral problems for tridiagonal N by N complex hamiltonians, Symmetry Integrability and Geometry: Methods and Applications, 28 pages, 2009.
  13. Manafov, M.D., Bala, B., Inverse spectral problems for tridiagonal N by N complex hamiltonians with spectral parameter in the initial conditions, Adıyaman Üniversitesi Fen Bilimleri Dergisi, 3(1), 20-27, 2013.
  14. Akhmedova, E.N., Huseynov, H.M., On eigenvalues and eigenfunctions of one class of Sturm-Liouville operators with discontinuous coefficients, Transactions of National Academy of Sciences of Azerbaijan Series of Physical-Technical and Mathematical Sciences, 23-4, 7-18, 2003.
  15. Akhmedova, E.N.