JournalsjstVol. 4, No. 2pp. 349–364

Spectral instability for even non-selfadjoint anharmonic oscillators

  • Raphaël Henry

    Université Paris-Sud, Orsay, France
Spectral instability for even non-selfadjoint anharmonic oscillators cover

Abstract

We study the instability of the spectrum for a class of non-selfadjoint anharmonic oscillators, estimating the behavior of the instability indices (\emph{i. e.} the norm of spectral projections) associated with the large eigenvalues of these oscillators. More precisely, we consider the operators

\CA(2k,θ)=d2dx2+eiθx2k\CA(2k,\theta) = -\frac{d^2}{dx^2}+e^{i\theta}x^{2k}

defined on L2(R)L^2(\mathbb{R}), with k1k\geq1 and θ<(k+1)π/2k|\theta|<(k+1)\pi/2k. We get asymptotic expansions for the instability indices, extending the results of \cite{Dav2} and \cite{DavKui}.

Cite this article

Raphaël Henry, Spectral instability for even non-selfadjoint anharmonic oscillators. J. Spectr. Theory 4 (2014), no. 2, pp. 349–364

DOI 10.4171/JST/72