Solving an integral for an unknown function

*To*: mathgroup at smc.vnet.net*Subject*: [mg124528] Solving an integral for an unknown function*From*: Mikael <mikaen.anderson.1969 at gmail.com>*Date*: Sun, 22 Jan 2012 07:28:49 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Dear All, I wonder if anyone could let me know if there is a general solution to the following problem in Mathematica. Suppose the functions g[u,w] and h[w] are known. I want to find a function f[u] such that Integrate[g[u,w]*f[u],{u,0,1}]=h[w]. In addition I know that Integrate[f[u],{u,0,1}]=2 and Integrate[u*f[u],{u,0,1}]=1. Is it possible to solve the above for the unknown function f[u]? Of course there might be several solutions but I would be happy to find one. Many thanks in advance for any suggestions. Mikael