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Journals / Cumhuriyet Üniversitesi Fen-Edebiyat Fakültesi Fen Bilimleri Dergisi / 2017 / Cilt: 38 - Sayı: 2

Inverse Problems for Dirac Operator with Boundary Conditions Involving A Herglotz-Nevanlinna function

Herglotz-Nevanlinna Fonksiyonu İçeren Sınır Koşullarına Sahip Dirac Operatörü için Ters Problemler

Yalçın GÜLDÜ
A Sinan ÖZKAN
Pages
204–218
Publication Date
2022-10-11
DOI
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AI Summary & Key Takeaways

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

Moreover, it is shown thatQ(x)is uniquely determined by the classical spectral data, i.e.,eigenvalues and normalising numbers.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we deal with the inverse problems for Dirac operator with rationally eigenvalue dependent boundarycondition and linearly eigenvalue dependent jump conditions.
📊
Key Findings & Data:We prove that whenQ(x)is known on??????,121then onlyone spectrum excluding a finite number of eigenvalues is sufficient to determineQ(x)on the interval?0,1?and the othercoefficients of the problem.
💡
Conclusion & Impact:Moreover, it is shown thatQ(x)is uniquely determined by the classical spectral data, i.e.,eigenvalues and normalising numbers.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

t. In this paper, we deal with the inverse problems for Dirac operator with rationally eigenvalue dependent boundarycondition and linearly eigenvalue dependent jump conditions. We prove that whenQ(x)is known on??????,121then onlyone spectrum excluding a finite number of eigenvalues is sufficient to determineQ(x)on the interval?0,1?and the othercoefficients of the problem. Moreover, it is shown thatQ(x)is uniquely determined by the classical spectral data, i.e.,eigenvalues and normalising numbers.

Özet

Bu makalede, sınır koşulları spektral parametreye rasyonel, süreksizlik koşulları ise lineer şekilde bağlı olan Dirac operatörü için ters problem ele alınmıştır. (½,1) aralığında Q(x) potansiyel fonksiyonu biliniyorken, tek spektrumun sonlu sayıda özdeğerlerin dışında (0,1) aralığında Q(x) potansiyel fonksiyonunu ve problemin diğer katsayılarını tek olarak belirlediği ispatlanmaktadır. Ayrıca, Q(x) fonksiyonunun klasik spektral veriler, yani özdeğerler ve normalleştirici sayılar yardımıyla tek olarak belirlendiği gösterilmektedir.

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Cite This Article

GÜLDÜ, Y., ÖZKAN, A. S. (2022). Inverse Problems for Dirac Operator with Boundary Conditions Involving A Herglotz-Nevanlinna function. Cumhuriyet Üniversitesi Fen-Edebiyat Fakültesi Fen Bilimleri Dergisi, Cilt: 38 - Sayı: 2, 204–218. https://ajindex.com/articles/480365

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References (1)

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