no. 4
On the trace of the wave group and regularity of potentials
Smith, Hart F.1
1Department of Mathematics University of Washington Seattle, WA 98195-4350 (USA)
Annales de l'Institut Fourier, Volume 73 (2023) no. 4, pp. 1453-1488

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:
Published online:
DOI: 10.5802/aif.3538
Classification: 58J45, 58J50, 46E35
Keywords: Trace, wave equation with potential.
Mots-clés : Trace, équation des ondes avec potentiel.

Smith, Hart F.  1

1 Department of Mathematics University of Washington Seattle, WA 98195-4350 (USA)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Smith, Hart F. On the trace of the wave group and regularity of potentials. Annales de l'Institut Fourier, Volume 73 (2023) no. 4, pp. 1453-1488. doi: 10.5802/aif.3538
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