1. The problem statement, all variables and given/known data Let V be the linear space of all real functions Differentiable on (0,1). If f is in V define g=T(f) to mean that g(t)=tf'(t) for all t in (0,1). Prove that every real λ is an eigenvalue for T, and determine the eigenfunctions corresponding to λ. 2. Relevant equations 3. The attempt at a solution All I know is that f'=λf and T(f)=λf in general. I tried substituting the variables, and I ended up with only t, which doesn't make sense.