Question: Let c(x) C[a, b] be a continuous function. Prove that the linear multiplication operator K[u) = c(x)u(x) is self-adjoint with respect to the L2

Let c(x) ∈ C°[a, b] be a continuous function. Prove that the linear multiplication operator K[u) = c(x)u(x) is self-adjoint with respect to the L2 inner product. What sort of boundary conditions need to be imposed?

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