Identifiability and stability of an inverse problem involving a Fredholm equation (Q746370)

The paper is concerned with the linear inverse problem of determining \(\rho=\rho(x)>0\) from the measurement of \(I[\rho](t)=\int_0^L K(t,x)\rho(x)dx\), where \(K(t,x)=F(c(t,x))\). Here, \(c(t,x)\) is a given function and \(F(x)=x^{n}/(x^n+a)\) with \(a>0\). The authors establish identifiability, stability and reconstruction results related to the simplified version of the problem with \(F(x)\) replaced by its appropriate step function approximations \(F_m(x)\).