Some Recent Developments in the Transmutation Operator Approach

Kravchenko, Vladislav V.; Sitnik, Sergei M.

doi:10.1007/978-3-030-35914-0_1

Cited by 11 publications

(9 citation statements)

References 32 publications

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“…We denote by Q 1 (L 0 ) the collection of operators B Θ whose eigenfunctions are given by relations (24). The corresponding set of the transformation operators is denoted by Γ 1 (L 0 ).…”

Section: Transformation Operatorsmentioning

confidence: 99%

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Nonlocal Problem with Multipoint Perturbations of the Birkhoff Strongly Regular Boundary Conditions for an Even-Order Differential Operator

2023

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We study spectral properties of a nonself-adjoint problem for a (2n ) th order operator of differentiation with nonlocal conditions representing multipoint perturbations of the Birkhoff strongly regular selfadjoint conditions. We establish sufficient conditions under which the system of eigenfunctions is complete and, under certain additional assumptions, forms a Riesz basis. We construct a set of transformation operators, each element of which maps the system of eigenfunctions of the unperturbed problem into the system of eigenfunctions of a certain isospectral problem. The cases of problems with Birkhoff regular and irregular two-point perturbations are analyzed. Finally, we establish conditions for the existence and uniqueness of the solution of the studied problem.

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“…We denote by Q 1 (L 0 ) the collection of operators B Θ whose eigenfunctions are given by relations (24). The corresponding set of the transformation operators is denoted by Γ 1 (L 0 ).…”

Section: Transformation Operatorsmentioning

confidence: 99%

“…Fundamental results in the spectral theory of operators of boundary-value problems for ordinary differential equations were obtained in [6-8, 11-14, 23, 25]. Foundations of the theory of transformation operators and its various applications were described in [10,24].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Problem with Multipoint Perturbations of the Birkhoff Strongly Regular Boundary Conditions for an Even-Order Differential Operator

2023

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“…Фундаментальні результати спектральної теорії операторів крайових задач для звичайних диференціальних рівнянь отримано в роботах [6-8, 11-14, 23, 25]. Основи теорії операторів перетворення та її різноманітні застосування висвітлено в роботах [10,24].…”

Section: нелокальна задача з багатоточковими збуреннями сильно регуля...unclassified

A nonlocal problem with multipoint perturbations of strongly regular Birkhoff boundary conditions for an even-order differential operator

Baranetskij¹,

Демків²,

Kalenyuk³

2020

Mat. Met. Fiz. Mekh. Polya

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“…And topic of this paper is also in a very tight connection with transmutation theory, cf. [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Multi-Dimensional Generalized Integral Transform in the Weighted Spaces of Summable Functions

Sitnik

Скоромник²,

Shlapakov³

2022

Lobachevskii J Math

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In this paper, we study a multi-dimensional generalized integral transformation. The functional and compositional properties of the integral transformation in spaces of summable functions are investigated. The scheme of study is similar to the process of constructing the theory of the H-transformation, in which the central place is given to the questions of bounded and oneto-one action of the corresponding integral operator in spaces of integrable functions with weight concentrated at zero and at infinity. Theory of the considered integral transformation in weighted spaces of summable functions is constructed.

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Some Recent Developments in the Transmutation Operator Approach

Cited by 11 publications

References 32 publications

Nonlocal Problem with Multipoint Perturbations of the Birkhoff Strongly Regular Boundary Conditions for an Even-Order Differential Operator

Nonlocal Problem with Multipoint Perturbations of the Birkhoff Strongly Regular Boundary Conditions for an Even-Order Differential Operator

A nonlocal problem with multipoint perturbations of strongly regular Birkhoff boundary conditions for an even-order differential operator

Multi-Dimensional Generalized Integral Transform in the Weighted Spaces of Summable Functions

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