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A non elliptic spectral problem related to the analysis of superconducting micro-strip lines

Anne-Sophie Bonnet-Bendhia, Karim Ramdani (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is devoted to the spectral analysis of a non elliptic operator A , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator A has been derived, we determine its continuous spectrum. Then, we show that A is unbounded from below and that it has a sequence of negative eigenvalues tending to - ∞ . Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some conditions...

A non elliptic spectral problem related to the analysis of superconducting micro-strip lines

Anne-Sophie Bonnet-Bendhia, Karim Ramdani (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is devoted to the spectral analysis of a non elliptic operator A , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator A has been derived, we determine its continuous spectrum. Then, we show that A is unbounded from below and that it has a sequence of negative eigenvalues tending to -∞. Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some...

A spectral study of an infinite axisymmetric elastic layer

Lahcène Chorfi (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators A n , n ∈ ℕ , in a suitable Hilbert space. We show that the essential spectrum of A n is an interval of type [ γ , + ∞ [ and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.

A spectral study of an infinite axisymmetric elastic layer

Lahcène Chorfi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present here a theoretical study of eigenmodes in axisymmetric elastic layers. The mathematical modelling allows us to bring this problem to a spectral study of a sequence of unbounded self-adjoint operators An, n ∈ ℕ , in a suitable Hilbert space. We show that the essential spectrum of An is an interval of type [ γ , + ∞ [ and that, under certain conditions on the coefficients of the medium, the discrete spectrum is non empty.

A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type

Evgenii Pustylnik (2001)

Czechoslovak Mathematical Journal

The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations.

Convergence of approximation methods for eigenvalue problem for two forms

Teresa Regińska (1984)

Aplikace matematiky

The paper concerns an approximation of an eigenvalue problem for two forms on a Hilbert space X . We investigate some approximation methods generated by sequences of forms a n and b n defined on a dense subspace of X . The proof of convergence of the methods is based on the theory of the external approximation of eigenvalue problems. The general results are applied to Aronszajn’s method.

Decomposition of operators with countable spectrum.

Lucas Jódar (1986)

Stochastica

Sufficient spectral conditions for the existence of a spectral decomposition of an operator T defined on a Banach space X, with countable spectrum, are given. We apply the results to obtain the West decomposition of certain Riesz operators.

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