no. 4
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, 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 
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.3538/

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