Search results for "47A10"

showing 2 items of 12 documents

Interior Eigenvalue Density of Jordan Matrices with Random Perturbations

2017

International audience; We study the eigenvalue distribution of a large Jordan block subject to a small random Gaussian perturbation. A result by E. B. Davies and M. Hager shows that as the dimension of the matrix gets large, with probability close to 1, most of the eigenvalues are close to a circle.We study the expected eigenvalue density of the perturbed Jordan block in the interior of that circle and give a precise asymptotic description.; Nous étudions la distribution de valeurs propres d’un grand bloc de Jordan soumis à une petite perturbation gaussienne aléatoire. Un résultat de E. B. Davies et M. Hager montre que quand la dimension de la matrice devient grande, alors avec probabilité…

[ MATH ] Mathematics [math]Jordan matrixSpectral theoryGaussian010102 general mathematicsMathematical analysisPerturbation (astronomy)Mathematics::Spectral Theory01 natural sciences010104 statistics & probabilityMatrix (mathematics)symbols.namesakesymbolsRandom perturbations[MATH]Mathematics [math]MSC: 47A10 47B80 47H40 47A550101 mathematicsDivide-and-conquer eigenvalue algorithmSpectral theoryEigenvalue perturbationEigenvalues and eigenvectorsNon-self-adjoint operatorsMathematics
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Resolvent estimates for elliptic quadratic differential operators

2011

Sharp resolvent bounds for non-selfadjoint semiclassical elliptic quadratic differential operators are established, in the interior of the range of the associated quadratic symbol.

quadratic differential operatorSemiclassical physics47A10 35P05 15A63 53D2215A6353D22spectrumMathematics - Spectral TheoryMathematics - Analysis of PDEsQuadratic equationFOS: Mathematicsnonselfadjoint operator35P05Quadratic differentialSpectral Theory (math.SP)ResolventMathematicsNumerical AnalysisMathematics::Operator AlgebrasApplied MathematicsMathematical analysisSpectrum (functional analysis)resolvent estimateMathematics::Spectral TheoryDifferential operator47A10Range (mathematics)FBI-Bargmann transformAnalysisAnalysis of PDEs (math.AP)
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