(c) Recall that P3(R) denotes the vector space over R of polynomials of degree ? 3 with real coefficients. Use the Riesz representation theorem to prove that for each t ? R we can find a unique polynomial qt ? P3(R) such that for every p ? P3(R) we have p(t) = ??¹ p(x)qt(x)dx. (d) What is the polynomial q1/2?
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