Stability of Fredholm Integral Equation of the First Kind in Reproducing Kernel Space (Communications in Mathematical Research, 2021)
It is well known that the problem on the stability of the solutions forFredholm integral equation of the first kind is an ill-posed problem in $C[a, b]$ or $L^2[a, b]$.In this paper, the representation of the solution for Fredholm integral equation of thefirst kind is given if it has a unique solution. The stability of the solution is provedin the reproducing kernel space, namely, the measurement errors of the experimentaldata cannot result in unbounded errors of the true solution. The computation ofapproximate solution is also stable with respect to $‖·‖_C$ or $‖· ‖_{L^2}$. A numericalexperiment shows that the method given in this paper is stable in the reproducingkernel space.