Local spectral deformation

Matthias Engelmann, Jacob Schach Møller, Morten Grud Rasmussen

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Resumé

We develop an analytic perturbation theory for eigenvalues with finite multiplicities, embedded into the essential spectrum of a self-adjoint operator H. We assume the existence of another self-adjoint operator A for which the family H θ = eiθAHe -iθA extends analytically from the real line to a strip in the complex plane. Assuming a Mourre estimate holds for i[H, A] in the vicinity of the eigenvalue, we prove that the essential spectrum is locally deformed away from the eigenvalue, leaving it isolated and thus permitting an application of Kato's analytic perturbation theory.

OriginalsprogEngelsk
TidsskriftAnnales de l'Institut Fourier
Vol/bind68
Udgave nummer2
Sider (fra-til)768-804
Antal sider39
ISSN0373-0956
StatusUdgivet - 2018

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Essential Spectrum
Self-adjoint Operator
Eigenvalue
Perturbation Theory
Real Line
Argand diagram
Strip
Multiplicity
Estimate
Family

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Engelmann, M., Møller, J. S., & Rasmussen, M. G. (2018). Local spectral deformation. Annales de l'Institut Fourier, 68(2), 768-804.
Engelmann, Matthias ; Møller, Jacob Schach ; Rasmussen, Morten Grud. / Local spectral deformation. I: Annales de l'Institut Fourier. 2018 ; Bind 68, Nr. 2. s. 768-804.
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Engelmann, M, Møller, JS & Rasmussen, MG 2018, 'Local spectral deformation', Annales de l'Institut Fourier, bind 68, nr. 2, s. 768-804.

Local spectral deformation. / Engelmann, Matthias ; Møller, Jacob Schach; Rasmussen, Morten Grud.

I: Annales de l'Institut Fourier, Bind 68, Nr. 2, 2018, s. 768-804.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Local spectral deformation

AU - Engelmann, Matthias

AU - Møller, Jacob Schach

AU - Rasmussen, Morten Grud

PY - 2018

Y1 - 2018

N2 - We develop an analytic perturbation theory for eigenvalues with finite multiplicities, embedded into the essential spectrum of a self-adjoint operator H. We assume the existence of another self-adjoint operator A for which the family H θ = eiθAHe -iθA extends analytically from the real line to a strip in the complex plane. Assuming a Mourre estimate holds for i[H, A] in the vicinity of the eigenvalue, we prove that the essential spectrum is locally deformed away from the eigenvalue, leaving it isolated and thus permitting an application of Kato's analytic perturbation theory.

AB - We develop an analytic perturbation theory for eigenvalues with finite multiplicities, embedded into the essential spectrum of a self-adjoint operator H. We assume the existence of another self-adjoint operator A for which the family H θ = eiθAHe -iθA extends analytically from the real line to a strip in the complex plane. Assuming a Mourre estimate holds for i[H, A] in the vicinity of the eigenvalue, we prove that the essential spectrum is locally deformed away from the eigenvalue, leaving it isolated and thus permitting an application of Kato's analytic perturbation theory.

M3 - Journal article

VL - 68

SP - 768

EP - 804

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

SN - 0373-0956

IS - 2

ER -

Engelmann M, Møller JS, Rasmussen MG. Local spectral deformation. Annales de l'Institut Fourier. 2018;68(2):768-804.