A Uniqueness Theorem for Bessel Operator from Interior Spectral Data

Şat, Murat; Panakhov, Etibar S.

doi:10.1155/2013/713654

Cited by 9 publications

(6 citation statements)

References 17 publications

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“…Yilmazer and Bas [7] introduced fractional solutions of a confluent hypergeometric equation by using N-fractional calculus operator. This method presents successful results for some singular differential equations [8,9]. And, we also apply this operator to the associated Legendre equation in this paper.…”

Section: Introductionmentioning

confidence: 89%

Fractional Solutions of the Associated Legendre Equation

Ozturk

2016

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi

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Section: Introductionmentioning

confidence: 89%

Fractional Solutions of the Associated Legendre Equation

Ozturk

2016

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi

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“…Mochizuki and Trooshin [20] showed that the spectral data of parts of two spectra and a set of values of eigenfunctions at some internal point suffice to determine the potential, and they addressed the interior inverse problem of Sturm-Liouville operators on the finite interval [0,1]. Afterwards, this technique has been used by some authors to survey the inverse problem of Sturm-Liouville operators in various forms [10,22,25,29,33]. Alongside this method, in [9], Hochstadt and Lieberman found the half inverse problem method and showed that if the potential is prescribed on [1/2, 1], one spectrum can uniquely determine the potential on the whole interval [0, 1].…”

Section: Introductionmentioning

confidence: 99%

Recovering differential pencils with spectral boundary conditions and spectral jump conditions

Khalili

Băleanu

2020

J Inequal Appl

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In this work, we discuss the inverse problem for second order differential pencils with boundary and jump conditions dependent on the spectral parameter. We establish the following uniqueness theorems: $(i)$ ( i ) the potentials $q_{k}(x)$ q k ( x ) and boundary conditions of such a problem can be uniquely established by some information on eigenfunctions at some internal point $b\in (\frac{\pi }{2},\pi )$ b ∈ ( π 2 , π ) and parts of two spectra; $(ii)$ ( i i ) if one boundary condition and the potentials $q_{k}(x)$ q k ( x ) are prescribed on the interval $[\pi /2(1-\alpha ),\pi ]$ [ π / 2 ( 1 − α ) , π ] for some $\alpha \in (0, 1)$ α ∈ ( 0 , 1 ) , then parts of spectra $S\subseteq \sigma (L)$ S ⊆ σ ( L ) are enough to determine the potentials $q_{k}(x)$ q k ( x ) on the whole interval $[0, \pi ]$ [ 0 , π ] and another boundary condition.

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“…They used similar techniques in [7]. This kind of problems for the Sturm-Liouville operator were formulated and studied in [12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%