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We improve the preceding results obtained by the first and the second authorsin [3]. They concern the stability issue of the inverse problem that consistsin determining the potential and the damping coefficient in a wave equationfrom an initial-to-boundary operator. We partially modify the arguments in [3]to show that actually we have H{\"o}lder stability instead of logarithmicstability.

H{\"o}lder stability in determining the potential and the damping coefficient in a wave equation