Linear Algebra Done Right · Problem 12

Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · riesz-representation

Problem

Find a polynomial

q \in \mathcal{P}_2(\mathbf{R})

such that

\int_0^1 p(x) \cos(\pi x)\, dx = \int_0^1 pq

for every

p \in \mathcal{P}_2(\mathbf{R})