Non-self-adjoint harmonic oscillator, compact semigroups and pseudospectra
| Venue: | J. Operator Theory |
| Citations: | 7 - 2 self |
BibTeX
@ARTICLE{Boulton_non-self-adjointharmonic,
author = {Lyonell S. Boulton},
title = {Non-self-adjoint harmonic oscillator, compact semigroups and pseudospectra},
journal = {J. Operator Theory},
year = {},
pages = {413--429}
}
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Abstract
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.
Citations
| 227 | Schrödinger operators with applications to quantum mechanics and global geometry - Cycon, Froese, et al. |
| 88 | Pseudospectra of linear operators - Trefethen - 1997 |
| 84 | One-parameter Semigroups - Davies - 1980 |
| 76 | Perturbation Theory for Linear Operators. 2nd edition - Kato - 1976 |
| 54 | Semi-classical analysis for the Schrödinger operator and applications - Helffer - 1988 |
| 27 | Semi-classical states for non-self-adjoint Schrödinger operators - Davies |
| 21 | Non-self-adjoint differential operators - Davies |
| 21 | the harmonic oscillator and complex resonances - Pseudo-spectra - 1999 |
| 12 | E B: Spectral instability for some Schrödinger operators - Aslanyan, Davies |
| 7 | C ∗ -algebra techniques in numerical analysis - Roch, Silbermann |
| 6 | B: Wild spectral behaviour of anharmonic oscillators - Davies - 2000 |
| 3 | On eigenfunction approximations for typical non-selfadjoint Schrödinger operators - Aslanyan, Davies - 1999 |
