Essential spectra of operator matrices and applications

Charfi, Salma; Jeribi, Aref; Moalla, Rihab

doi:10.1002/mma.2819

Cited by 22 publications

(6 citation statements)

References 22 publications

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“…More specific perturbations results are stated until the paper where they are used to describe the Fredholm, right and left Fredholm perturbations of the difference between the resolvents of two block operator matrices which ensure the stability on their M -essential spectra under weaker conditions than proved in the papers of [4,14,25]. All the results are new and…”

Section: Discussionmentioning

confidence: 99%

“…In this direction some issues may be found in the literature, we can quote for example [1,2,10,16,24]. Recently, an account research and a wide panorama of methods to investigate the spectral theory of block operator matrices is given in [3,4,5,11,14,25]. More precisely, the description of various essential spectra of a block operator matrix L appears in [3,5,11,14] to improve and generalize some results given by [1,2,24] for block operator matrices in Banach spaces under some compactness assumptions.…”

Section: Introductionmentioning

confidence: 99%

“…More precisely, the description of various essential spectra of a block operator matrix L appears in [3,5,11,14] to improve and generalize some results given by [1,2,24] for block operator matrices in Banach spaces under some compactness assumptions. However, it should be noted that several results for the authors cited in the papers of [1,2,4,14,24] are aimed at providing methods for dealing with spectral theory for operator in the form L 0 − λM where M = I.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of this work consists principally in extending results given in [4] and we concern ourselves exclusively with the investigation of some Messential spectra of unbounded 2 × 2 block operator matrices for pencils of the form L 0 − λM, where M is a bounded operator defined on the product of two Banach spaces X × Y under a coupling condition between the two components of its elements.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the use of the M -resolvent, the Fredholm perturbations theory and the lower factorization allows us to formulate some supplements to many results presented in [4,14] and to ameliorate the description of the Messential spectra of two-group transport equations without knowing the totality of the relative essential spectra of the operator A, but only the relative essential spectra of its restriction which is more general than the one provided by [4,14]. The present paper consists of four sections: In Section 2, we present some basic notations and auxiliary lemmas connected to the main body of the paper.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On Relative Essential Spectra of Block Operator Matrices and Application

Charfi¹,

Walha²

2016

Bulletin of the Korean Mathematical Society

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Relative Essential Spectra of Block Operator Matrices and Application

Charfi¹,

Walha²

2016

Bulletin of the Korean Mathematical Society

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On coupled semilinear evolution systems: Techniques on fractional powers of 4×4$4\times 4$ matrices and applications

Belluzi,

Bezerra,

Nascimento

2024

Mathematische Nachrichten

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In this paper, we provide several techniques to explicitly calculate fractional powers of operator matrices focusing on creating a theory that can be applied to distinct situations. To illustrate the abstract results developed, we consider its application in systems of coupled reaction–diffusion equations and in (strongly damped) wave equations. We also discuss how these techniques can be applied to higher order matrices and we specifically calculate the fractional powers of a operator matrix associated to a weakly coupled system of wave equation. In addition, we deal with the applicability of this analysis with respect to solvability, stabilization, regularity, smooth dynamics, and connection with evolutionary classic equation and its fractional counterpart.

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Introduction

Jeribi¹

2015

Spectral Theory and Applications of Linear Operators and Block Operator Matrices

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IntroductionThis book is devoted to some recent mathematical developments which cover several topics including Cauchy problem, Fredholm operators, spectral theory, and block operator matrices, both dealing with linear operators. Of course, these topics play a crucial role in many branches of mathematics and also in numerous applications as they are intimately related to the stability of the underlying physical systems.One of the objectives of this book is the study of the classical Riesz theory of polynomially compact operators, in order to establish the existence results of the second kind operator equations, hence allowing to describe the spectrum, multiplicities, and localization of the eigenvalues of polynomially compact operators. Fredholm theory and perturbation results are also widely investigated. The description of the large time behavior of solutions to an abstract Cauchy problem on Banach spaces without restriction on the initial data is studied. Further, the essential state of the art of research and essential pseudo-spectra of closed, densely defined, and linear operators subjected to additive perturbations is outlined. The spectral theory of block operator matrices is of major interest, since it describes coupled systems of partial differential equations of mixed order and type. For this reason, an important part of this book is devoted to develop essential spectra of 2 2 and 3 3 block operator matrices. Based on the spectral graph theory (which is an active research area), we are interested in the study of the adjacency matrix and the discrete Laplacian acting on forms. Most of the results of this book are motivated by physical transport problems for which we address our applications at the end of the book. Now, let us describe its contents.

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Essential spectra of operator matrices and applications

Abstract: The main goal of this paper is to give a characterization of Wolf, Schechter, and Browder essential spectra of (2 × 2) matrix operator on a Banach space. Furthermore, we apply the obtained results to transport equations. Copyright © 2013 John Wiley & Sons, Ltd.

Cited by 22 publications

References 22 publications

On Relative Essential Spectra of Block Operator Matrices and Application

On Relative Essential Spectra of Block Operator Matrices and Application

On coupled semilinear evolution systems: Techniques on fractional powers of 4×4$4\times 4$ matrices and applications

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