From Mendeleev to Fourier

The previous post looked at an inequality discovered by Dmitri Mendeleev and generalized by Andrey Markov: Theorem (Markov): If P(x) is a real polynomial of degree n, and |P(x)| ≤ 1 on [−1, 1] then |P′(x)| ≤ n² on [−1, 1]. If P(x) is a trigonometric polynomial then Bernstein proved that the bound decreases from n² to n. Theorem […] The post From Mendeleev to Fourier first appeared on John D. Cook.