On the trace of the wave group and regularity of potentials. (Sur la trace du propagateur des ondes et régularité du potentiel.) (English. French summary) Zbl 1518.35472
Summary: 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 \(m\).
MSC:
| 35L15 | Initial value problems for second-order hyperbolic equations |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 47D06 | One-parameter semigroups and linear evolution equations |
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