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Spectral Asymptotics of the Non‐Self‐Adjoint Harmonic Oscillator
Author(s) -
Davies E. B.,
Kuijlaars A. B. J.
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610704005381
Subject(s) - harmonic oscillator , mathematics , mathematical analysis , constant (computer programming) , norm (philosophy) , spectral properties , harmonic , asymptotic expansion , mathematical physics , pure mathematics , physics , quantum mechanics , computer science , political science , astrophysics , law , programming language
An explicit asymptotic formula is obtained for the norms of the spectral projections of the non‐self‐adjoint harmonic oscillator H. It is deduced that the spectral expansion of e ‐Ht is norm convergent if and only if t is greater than a certain explicit positive constant.