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In this paper, we prove a conditional H\"older stability estimate for theinverse spectral problem of the biharmonic operator. The proof employs theresolvent estimate and a Weyl-type law for the biharmonic operator which wereobtained by the authors in \cite{LYZ}. This work extends nontrivially theresult in \cite{stefanov} from the second order Schr\"{o}dinger operator to thefourth order biharmonic operator.

Stability for the multi-dimensional Borg--Levinson theorem of the biharmonic operator