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

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

 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 \[4\] and \[5\].

Spectral instability for even non-selfadjoint anharmonic oscillators

Raphaël Henry

Abstract

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