Spectral instability of some non-selfadjoint anharmonic oscillators

Raphaël Henry

Spectral instability of some non-selfadjoint anharmonic oscillators

Spectral Theory 2013-01-23 v1

Authors: Raphaël Henry

Abstract

The purpose of this Note is to highlight the spectral instability of some non-selfadjoint differential operators, by studying the growth rate of the norms of the spectral projections $\Pi_n$ associated with their eigenvalues. More precisely, we are concerned with the complex Airy operator and even anharmonic oscillator. We get asymptotic expansions for the norm of the spectral projections associated with the large eigenvalues, extending the results of Davies and Davies-Kuijlaars.

Keywords

spectral instability non-selfadjoint operators anharmonic oscillator complex Airy operator spectral projections asymptotic expansions

Cite

@article{arxiv.1301.5192,
  title  = {Spectral instability of some non-selfadjoint anharmonic oscillators},
  author = {Raphaël Henry},
  journal= {arXiv preprint arXiv:1301.5192},
  year   = {2013}
}

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