The Bohr–Favard inequality is an inequality appearing in a problem of Harald Bohr[1] on the boundedness over the entire real axis of the integral of an almost-periodic function.
The ultimate form of this inequality was given by Jean Favard;[2] the latter materially supplemented the studies of Bohr, and studied the arbitrary periodic function
with continuous derivative
for given constants
which are natural numbers.
The accepted form of the Bohr–Favard inequality is
with the best constant
The Bohr–Favard inequality is closely connected with the inequality for the best approximations of a function and its
th derivative by trigonometric polynomials of an order at most
and with the notion of Kolmogorov's width in the class of differentiable functions (cf.
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