On the completeness of systems of root functions of differential operators of fractional order with matrix coefficients

Agibalova, Anna V.

doi:10.1134/s0001434610070266

Cited by 4 publications

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“…In his paper [6] M. M. Dzhrbashian wrote, that "the question about the completeness of the systems of eigenfunctions of the operator A ρ or a finer question about whether these systems compose a basis in L 2 (0, 1), has a certain interest but its solving is apparently associated with significant analytic difficulties". The questions of the completeness of the systems of eigenfunctions and associated functions for similar problems were studied by A. V. Agibalova in [7,8]. Undoubtedly, we shall note the fundamental results of M. M. Malamud and L. L. Oridoroga [9][10][11][12] obtained in this direction.…”

Section: Resultsmentioning

confidence: 93%

On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order

Aleroev

2019

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The present paper is devoted to the spectral analysis of operators induced by fractional differential equations and boundary conditions of Sturm-Liouville type. It should be noted that these operators are non-self-adjoint. The spectral structure of such operators has been insufficiently explored. In particular, a study of the completeness of systems of eigenfunctions and associated functions has begun relatively recently. In this paper, the completeness of the system of eigenfunctions and associated functions of one class of non-self-adjoint integral operators corresponding boundary value problems for fractional differential equations is established. The proof is based on the well-known Theorem of M.S. Livshits on the spectral decomposition of linear non-self-adjoint operators, as well as on the sectoriality of the fractional differentiation operator. The results of Dzhrbashian-Nersesian on the asymptotics of the zeros of the Mittag-Leffler function are used.

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Section: Resultsmentioning

confidence: 93%

On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order

Aleroev

2019

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“…We shall note the papers of M.M. Malamud [12][13][14][15] and his students devoted to the study of the problem of completeness of systems of eigen and associated functions of boundary-value problems for fractional-differential equations. These studies are essentially based on the well-known analogue of M. A. Neimark's theorem [16].…”

Section: Application Of the Obtained Results To Study The Problem Of ...mentioning

confidence: 99%

Spectral Analysis of One Class of Positive-Definite Operators and Their Application in Fractional Calculus

Matseevich,

Aleroev

2023

Mathematics

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Symmetric differential operators of fractional order and their extensions

Tokmagambetov

Torebek

2018

Trans. Moscow Math. Soc.

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On the completeness of systems of root functions of differential operators of fractional order with matrix coefficients

Cited by 4 publications

References 0 publications

On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order

On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order

Spectral Analysis of One Class of Positive-Definite Operators and Their Application in Fractional Calculus

Symmetric differential operators of fractional order and their extensions

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