# Spectral instability for even non-selfadjoint anharmonic oscillators

### Raphaël Henry

Université Paris-Sud, Orsay, France

## 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

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

defined on $L^2(\mathbb{R})$, with $k\geq1$ and $|\theta|<(k+1)\pi/2k$. 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