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

We prove for the first time a conditional H{o}lder stability related to the multi-dimensional Borg--Levinson theorem, which is concerned with determining a potential from spectral data for the biharmonic operator. The proof depends on the theory of scattering resonances to obtain the resolvent estimate and a Weyl-type law for the biharmonic operator.