= Bernstein inequality for trigonometric polynomials
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{title2=$\|T_n'\|_\infty\le n\|T_n\|_\infty$}
A <trigonometric polynomial> of degree at most $n$ obeys the displayed derivative bound. Iteration gives $\|T_n^{(r)}\|_\infty\le n^r\|T_n\|_\infty$. Applied to differences of approximants at dyadic degrees, this inequality underlies the <inverse theorem for trigonometric approximation>. It differs from the endpoint-weighted <Bernstein inequality for algebraic polynomials>.
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