1999/09/29 by Lyonell Boulton, Lyonell S. Boulton, Boulton, Lyonell S. · 1 citation
Mathematics · #34L40 #47A75 #47D06 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical functions and polynomials #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.FA #math.SP #msc:34L40 #msc:47A75 #msc:47D06
paper · pdf · doi:10.48550/arxiv.math/9909179
22 pages, LaTeX 2e
openalex publication_date 1999/09/29 · arxiv created 1999/10/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.