On the trace of the wave group and regularity of potentials
Smith, Hart F.1
1 Department of Mathematics University of Washington Seattle, WA 98195-4350 (USA)
Annales de l'Institut Fourier, Online first, 36 p.

We consider the wave equation with a compactly supported, real-valued bounded potential, and show that the relative trace of the associated evolution group admits an asymptotic expansion to order m+2 if and only if the potential belongs to the Sobolev space of order m.

Nous considérons l’équation des ondes avec un potentiel borné, à support compact et à valeurs réelles, et montrons que la trace régularisée de l’opérateur d’évolution associé admet un développement asymptotique à l’ordre m+2 si et seulement si le potentiel appartient à l’espace de Sobolev d’ordre m.

Received:
Revised:
Accepted:
Online First:
DOI: 10.5802/aif.3538
Classification: 58J45, 58J50, 46E35
Keywords: Trace, wave equation with potential.
Keywords: Trace, équation des ondes avec potentiel.
Smith, Hart F. 1

1 Department of Mathematics University of Washington Seattle, WA 98195-4350 (USA) 
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Smith, Hart F. On the trace of the wave group and regularity of potentials. Annales de l'Institut Fourier, Online first, 36 p.

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