On localization of the spectrum of non-self-adjoint differential operators

Valeev, N. F.

doi:10.1007/s10958-008-0144-7

Cited by 3 publications

(2 citation statements)

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“…The essential spectrum of various singular matrix differential operators is investigated in [1,4,8,14,17,19]. In particular, in [14] the authors consider a matrix differential operator with singular entries which arises in magnetohydrodynamics.…”

Section: Introductionmentioning

confidence: 99%

“…By means of the asymptotic Hain-Lüst operator and some pseudodifferential operator techniques, they determine the essential spectrum of that operator. In [19], the authors consider the problem of localization of the spectrum of nonselfadjoint differential operators on unbounded domains with power coefficients. To find the location of spectrum points in the complex plane, they use isospectral deformations of differential operators and the properties of families of closed operators analytic in the Kato sense.…”

Section: Introductionmentioning

confidence: 99%

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Bounds for the spectrum of a matrix differential operator with a damping term

Gil’

2010

Z. Angew. Math. Phys.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bounds for the spectrum of a matrix differential operator with a damping term

Gil’

2010

Z. Angew. Math. Phys.

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A primer on eigenvalue problems of non-self-adjoint operators

Kumar,

Hiremath,

Manzetti

2024

Anal.Math.Phys.

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An estimate for the resolvent of a non-self-adjoint differential operator on the half-line

Gil

2011

Journal of Mathematical Physics

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We consider the operator defined by \documentclass[12pt]{minimal}\begin{document}$(T_0y)(x)=-y^{\prime \prime }+ q(x)y\;\;(x>0)$\end{document}(T0y)(x)=−y′′+q(x)y(x>0) on the domain Dom (T0) = {f ∈ L2(0, ∈fty): f′′ ∈ L2(0, ∈fty), f(0) = 0}. Here q(x) = p(x) + ib(x), where p(x) and b(x) are real functions satisfying the following conditions: b(x) is bounded on [0, ∞), there exists the limit b0 ≔ limx → ∞b(x) and b(x) − b0 ∈ L2(0, ∈fty). In addition, \documentclass[12pt]{minimal}\begin{document}$\inf _x p(x)> \sup _x |b_1(x)|$\end{document}infxp(x)>supx|b1(x)|. We derive an estimate for the norm of the resolvent of T0, as well as prove that (T0 − ib0I)−1 is a sum of a normal operator and a quasinilpotent one, and these operators have the same invariant subspaces.

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On localization of the spectrum of non-self-adjoint differential operators

Cited by 3 publications

References 1 publication

Bounds for the spectrum of a matrix differential operator with a damping term

Bounds for the spectrum of a matrix differential operator with a damping term

A primer on eigenvalue problems of non-self-adjoint operators

An estimate for the resolvent of a non-self-adjoint differential operator on the half-line

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