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Bifurcation from the essential spectrum [PDF]
Lecture Notes in Mathematics, 1983 This report surveys some of the results that have been obtained during the past twenty years concerning bifurcation from a point in the essential spectrum of the linearization of a nonlinear equation. This means that the linearization is not a Fredholm operator and so, even locally, the problem cannot be reduced to an equivalent finite dimensional ...
C A Stuart, Stuart C A
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Decomposing the essential spectrum
Journal of Functional Analysis, 2009 We use C*-algebra theory to provide a new method of decomposing the eseential spectra of self-adjoint and non-self-adjoint Schrodinger operators in one or more space dimensions.
E B Davies
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A note on the discrete Schrödinger operator with a perturbed periodic potential [PDF]
Opuscula Mathematica, 2010 The aim of this paper is to study the spectrum of the one-dimensional discrete Schrödinger operator with a perturbed periodic potential. We obtain natural conditions under which this perturbation preserves the essential spectrum of the considered ...
Beata Strack
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On the spectrum of periodic perturbations of certain unbounded Jacobi operators [PDF]
Opuscula Mathematica, 2016 It is known that a purely off-diagonal Jacobi operator with coefficients \(a_n=n^{\alpha}\), \(\alpha\in(0,1]\), has a purely absolutely continuous spectrum filling the whole real axis.
Jaouad Sahbani
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Hildebrandt's theorem for the essential spectrum [PDF]
Opuscula Mathematica, 2015 We prove a variant of Hildebrandt's theorem which asserts that the convex hull of the essential spectrum of an operator \(A\) on a complex Hilbert space is equal to the intersection of the essential numerical ranges of operators which are similar to \(A\
Janko Bračič, Cristina Diogo
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Современная математика: Фундаментальные направления, 2023 In this paper, we study a problem of normal oscillations of a homogeneous mixture of several viscous compressible fluids filling a bounded domain of three-dimensional space with an infinitely smooth boundary.
D. A. Zakora
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New Characterizations of the Jeribi Essential Spectrum
International Journal of Analysis and Applications, 2023 In this paper, we give several characterizations of the Jeribi essential spectrum of a bounded linear operator defined on a Banach space by using the notion of almost weakly compact operators.
Belabbaci Chafika
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The essential spectrum of canonical systems [PDF]
Journal of Approximation Theory, 2020 We study the minimum of the essential spectrum of canonical systems $Ju'=-zHu$. Our results can be described as a generalized and more quantitative version of the characterization of systems with purely discrete spectrum, which was recently obtained by Romanov and Woracek [6]. Our key tool is oscillation theory.
Christian Remling, Kyle Scarbrough
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Discontinuities Cause Essential Spectrum
Communications in Mathematical Physics, 2022 AbstractWe study transfer operators associated to piecewise monotone interval transformations and show that the essential spectrum is large whenever the Banach space bounds$$L^\infty $$L∞and the transformation fails to be Markov. Constructing a family of Banach spaces we show that the lower bound on the essential spectral radius is optimal.
Oliver Butterley +2 more
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The Variation of Browder's Essential Spectrum [PDF]
Proceedings of the American Mathematical Society, 1975 This paper is devoted to giving various conditions concerning small perturbation of linear operators which imply the continuous variation of the Browder essential spectrum in the Hausdorff topology on the complex plane.
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