Favard theorem

From Encyclopedia of Mathematics
Jump to: navigation, search

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. Yu.N. Subbotin (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098