Spectral instability for even non-selfadjoint anharmonic oscillators

TL;DR

This paper investigates the spectral instability of non-selfadjoint anharmonic oscillators by deriving asymptotic expansions for their instability indices, extending previous theoretical results.

Contribution

It provides new asymptotic formulas for the instability indices of large eigenvalues in non-selfadjoint anharmonic oscillators, advancing spectral instability analysis.

Findings

Asymptotic expansions for instability indices derived

Extended previous results of Davies and Davies-Kuijlaars

Enhanced understanding of spectral projection norms in non-selfadjoint operators

Abstract

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. We get asymptotic expansions for the instability indices, extending the results of Davies and Davies-Kuijlaars.