Relatively Bounded Perturbations of Correct Restrictions and Extensions of Linear Operators

Biyarov, B. N.; Abdrasheva, Gulnara

doi:10.1007/978-3-319-67053-9_20

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Cited by 3 publications

(3 citation statements)

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“…In this section, we present some results for correct restrictions and extensions [3] which are used in Section 3.…”

Section: Preliminariesmentioning

confidence: 99%

Similar transformation of one class of correct restrictions

Biyarov

2021

Preprint

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“…In this section, we present some results for correct restrictions and extensions [3] which are used in Section 3.…”

Section: Preliminariesmentioning

confidence: 99%

Similar transformation of one class of correct restrictions

Biyarov

2021

Preprint

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“…In this section, we present some results for correct restrictions and extensions [4] which are used in Section 3. Let L 0 be some minimal operator, and let M 0 be another minimal operator related to L 0 by the equation (L 0 u, v) = (u, M 0 v) for all u ∈ D(L 0 ) and v ∈ D(M 0 ).…”

Section: Preliminariesmentioning

confidence: 99%

On the number of eigenvalues of correct restrictions and extensions for the Laplace operator

Biyarov¹,

Abdrasheva²,

Toleshbay³

2018

AIP Conference Proceedings

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The work is devoted to the study of Laplace operator when the potential is a singular generalized function and plays the role of a singular perturbation of a Laplace operator. Abstract theorem obtained earlier by the authors B.N. Biyarov and G.K. Abdrasheva applies to this. The main purpose of the study is the spectral issue. Singular perturbations for differential operators have been studied by many authors for the mathematical substantiation of solvable models of quantum mechanics, atomic physics, and solid state physics. In all these cases, the problems were self-adjoint. In this paper, we consider non-self-adjoint singular perturbation problems. A new method has been developed that allows investigating the considered problems.

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“…for any f ∈ X. Our approach is based on the theory of the extensions of linear operators in Banach spaces [1]. Problems (7), ( 8) are solved by using the inverse…”

Section: Introductionmentioning

confidence: 99%

Integro-Differential Equations Embodying Powers of a Differential Operator

Parasidis

Providas²

2019

Vestnik of Samara University. Natural Science Series

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We establish solvability and correctness criteria for two Fredholm type linear integro-diﬀerential operators B2, B4 encompassing up to second and fourth powers, respectively, of a diﬀerential operator A� with aknown inverse I = A�−1. We also derive explicit solution formulae to corresponding initial and boundary value problems by using the inverse of the diﬀerential operator. The approach is based on the theory of the extensions of linear operators in Banach spaces. Three example problems for ordinary and partial integro-diﬀerential operators are solved.

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Relatively Bounded Perturbations of Correct Restrictions and Extensions of Linear Operators

Cited by 3 publications

References 2 publications

Similar transformation of one class of correct restrictions

Similar transformation of one class of correct restrictions

On the number of eigenvalues of correct restrictions and extensions for the Laplace operator

Integro-Differential Equations Embodying Powers of a Differential Operator

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