It is found that the asymptotical density of zeros of a system of orthogonal polynomials whose weight function belongs to a wide class of distribution functions has the expression ρ(x) = π-1 (1 - x2)-1/2. This result is shown in two completely different ways: (1) from a Szegö theorem and (2) from a Geronimus theorem and a finding recently obtained by the author in a context of Jacobi matrices.
@article{urn:eudml:doc:39771,
title = {On a Szeg\"o's theorem of orthogonal polynomials.},
journal = {Revista Matem\'atica Hispanoamericana},
volume = {39},
year = {1979},
pages = {277},
zbl = {0457.42010},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39771}
}
Sánchez Dehesa, Jesús. On a Szegö's theorem of orthogonal polynomials.. Revista Matemática Hispanoamericana, Tome 39 (1979) p. 277. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39771/