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1 vote

Understanding quadrature rule of a function multiplied by another $C^{\infty}$ function

If I understand your question correctly, we could have $g(x_j) = 0$ for all $j = 1, \ldots, n$. Thus, $Q_n[f g] = 0$. Further, if $f$ is a low degree polynomial, the right-hand side of (1) vanishes. H …
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