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Pseudo-spectra, the harmonic oscillator and complex resonances. (English) Zbl 0931.70016

Summary: We prove that nonselfadjoint harmonic and anharmonic oscillator operators have nontrivial pseudospectra. As a consequence, the computation of high-energy resonances by the dilation analyticity technique is not numerically stable.

MSC:

70J10 Modal analysis in linear vibration theory
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
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