Eigenfunction expansions of a quadratic pencil of differential operator with periodic generalized potential

Manafov, Manaf Dzh.; Kablan, Abdullah

doi:10.14232/ejqtde.2013.1.76

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Cited by 3 publications

(1 citation statement)

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“…The paper [12] is devoted to the variational theory of the spectrum of operator pencils with self-adjoint operators. A quadratic pencil of differential operators with periodic generalized potential is considered in [13]. The fold completeness of a system of root vectors of a system of unbounded polynomial operator pencils in Banach spaces is investigated in [14].…”

Section: Introduction and Notationmentioning

confidence: 99%

Norm estimate for the inverse of a linear pencil with Hilbert–Schmidt operators

Gil’

2014

Applicable Analysis

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Let H be a Hilbert space with the unit operator I . The paper deals with the pencil T (z) = A + z B (z ∈ C), where A and B are Hilbert-Schmidt operators in H . We suggest a norm estimate for the inverse of I − T (z). By that estimate, bounds for the spectra of I − T (.) are established and perturbations by bounded operators are investigated. Applications to boundary value problems are also discussed.

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Section: Introduction and Notationmentioning

confidence: 99%

Norm estimate for the inverse of a linear pencil with Hilbert–Schmidt operators

Gil’

2014

Applicable Analysis

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Parseval equality of discrete Sturm-Liouville equation with periodic generalized function potentials

Manafov¹,

Kablan²,

Bala³

2018

AIP Conference Proceedings

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Prüfer Analysis of Periodic Singular Sturm–liouville Problem With Piecewise Characteristic

Cetin¹,

Kablan²,

Manafov³

2022

Fractals

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Prüfer transformation is more effective and flexible in studying the spectral analysis of boundary value problem than using the classical methods in operator theory. The goal of this paper is to study Prüfer approach to spectral analysis of periodic Sturm–Liouville problem with transmission condition. Since we are dealing with a singular problem, the characteristic function we obtained is a piecewise function. At the end of the study, the existence of eigenvalues of investigated problem by using Prüfer transformation is given.

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Eigenfunction expansions of a quadratic pencil of differential operator with periodic generalized potential

Cited by 3 publications

References 0 publications

Norm estimate for the inverse of a linear pencil with Hilbert–Schmidt operators

Norm estimate for the inverse of a linear pencil with Hilbert–Schmidt operators

Parseval equality of discrete Sturm-Liouville equation with periodic generalized function potentials

Prüfer Analysis of Periodic Singular Sturm–liouville Problem With Piecewise Characteristic

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