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Let V be the linear space of all real polynomials p(x) of degree < n. If p ∈ V, define q = T(p) to mean that q(t) = p(t + 1) for all real t. Prove that T has only the eigenvalue 1. What are the eigenfunctions belonging to this eigenvalue? What I did was T(p)= (lamda) p = q (Lamda) p(t+1) =...

Homework Statement 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.Homework Equations The Attempt...