Non-self-adjoint harmonic oscillator, compact semigroups and pseudospectra

Details Non-self-adjoint harmonic oscillator, compact semigroups and pseudospectra Non-self-adjoint harmonic oscillator, compact semigroups and pseudospectra

1999-09-29

arxiv.org/abs/math/9909179v2

Mathematics

Spectral Theory

22 pages, LaTeX 2e

Scientific paper

We provide new information concerning the pseudospectra of the complex harmonic oscillator. Our analysis illustrates two different techniques for getting resolvent norm estimates. The first uses the JWKB method and extends for this particular potential some results obtained recently by E.B. Davies. The second relies on the fact that the bounded holomorphic semigroup generated by the complex harmonic oscillator is of Hilbert-Schmidt type in a maximal angular region. In order to show this last property, we deduce a non-self-adjoint version of the classical Mehler's formula.

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