Favard theorem

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on orthogonal systems

If the following recurrence relation holds for real numbers and :

then there is a function of bounded variation such that

It was established by J. Favard [1]. Sometimes this result is also linked with the name of J. Shohat.


[1] J. Favard, "Sur les polynomes de Tchebicheff" C.R. Acad. Sci. Paris , 200 (1935) pp. 2052–2053
[2] G. Szegö, "Orthogonal polynomials" , Amer. Math. Soc. (1975)
How to Cite This Entry:
Favard theorem. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by Yu.N. Subbotin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article