Non-self-adjoint harmonic oscillator, compact semigroups and pseudospectra
谱理论
2007-05-23 v2 泛函分析
摘要
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.
引用
@article{arxiv.math/9909179,
title = {Non-self-adjoint harmonic oscillator, compact semigroups and pseudospectra},
author = {Lyonell S. Boulton},
journal= {arXiv preprint arXiv:math/9909179},
year = {2007}
}
备注
22 pages, LaTeX 2e