(a) Prove that the operation Ma[u(x)] = a(x)u(x) of multiplication by a fixed continuous function a(x) defines a self-adjoint linear operator on the function space C0[a, b] with respect to the L2 inner product.
(b) Is Ma also self-adjoint with respect to the weighted inner product

Transcribed Image Text:

《f, g))= | f(x) g(x) w(x) dx?