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}.

Spectral instability for even non-selfadjoint anharmonic oscillators

Raphaël Henry

Abstract

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