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SPECTRAL ASYMPTOTICS OF THE NON-SELF-ADJOINT HARMONIC OSCILLATOR

Published online by Cambridge University Press:  01 October 2004

E. B. DAVIES  and
A. B. J. KUIJLAARS
E. B. DAVIES
Affiliation:
Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdome.brian.davies@kcl.ac.uk
A. B. J. KUIJLAARS
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgiumarno.kuijlaars@wis.kuleuven.ac.be
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Abstract

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 $\rme^{-Ht}$ is norm convergent if and only if $t$ is greater than a certain explicit positive constant.

Keywords

34M1034L0547E0533C4534Exx
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 70 , Issue 2 , October 2004 , pp. 420 - 426
Copyright
The London Mathematical Society 2004

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