# Favard inequality

From Encyclopedia of Mathematics

The inequality

(*) |

where

and the function is orthogonal to every trigonometric polynomial of order not exceeding . For inequality (*) was proved by H. Bohr (1935), so it is also called the Bohr inequality and the Bohr–Favard inequality. For an arbitrary positive integer inequality (*) was proved by J. Favard [1].

#### References

[1] | J. Favard, "Sur l'approximation des fonctions périodiques par des polynomes trigonométriques" C.R. Acad. Sci. Paris , 203 (1936) pp. 1122–1124 |

[2] | V.M. Tikhomirov, "Some problems in approximation theory" , Moscow (1976) (In Russian) |

#### Comments

For a definition of the space cf. Favard problem.

**How to Cite This Entry:**

Favard inequality. Yu.N. Subbotin (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Favard_inequality&oldid=15703

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098