Description:
We deal with locally ill-posed nonlinear operator equations F(x) = y in L^2(0,1),where the Fréchet derivatives A = F'(x_0) of the nonlinear forward operator F arecompact linear integral operators A = M ◦ J with a multiplication operator Mwith integrable multiplier function m and with the simple integration operator J.In particular, we give examples of nonlinear inverse problems in natural sciencesand stochastic finance that can be written in such a form with linearizations thatcontain multiplication operators. Moreover, we consider the corresponding ill-posedlinear operator equations Ax = y and their degree of ill-posedness. In particular,we discuss the fact that the noncompact multiplication operator M has only arestricted influence on this degree of ill-posedness even if m has essential zeros ofvarious order.