Recovering the fragmentation rate in the growth-fragmentation equation

Abstract We consider the inverse problem of determining fragmentation rate from noisy measurements in growth-fragmentation equation. use Fourier transform theory on locally compact groups to treat this for general probabilities. develop a regularization method based spectral filtering, which allows us deal with weighted L 2 spaces. As result, we obtain error order $O(\varepsilon^{\frac{2m}{2m+1}})$?> O ( ε m + 1 stretchy="false">) , where ɛ is noise level and m > 0 priori regularity rate.