Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2004) no. 4, pp. 408-420
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Leonid Golinskii. Absolutely continuous measures on the unit circle with sparse Verblunsky coefficients. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2004) no. 4, pp. 408-420. http://geodesic.mathdoc.fr/item/JMAG_2004_11_4_a2/
@article{JMAG_2004_11_4_a2,
author = {Leonid Golinskii},
title = {Absolutely continuous measures on the unit circle with sparse {Verblunsky} coefficients},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {408--420},
year = {2004},
volume = {11},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JMAG_2004_11_4_a2/}
}
TY - JOUR
AU - Leonid Golinskii
TI - Absolutely continuous measures on the unit circle with sparse Verblunsky coefficients
JO - Žurnal matematičeskoj fiziki, analiza, geometrii
PY - 2004
SP - 408
EP - 420
VL - 11
IS - 4
UR - http://geodesic.mathdoc.fr/item/JMAG_2004_11_4_a2/
LA - en
ID - JMAG_2004_11_4_a2
ER -
%0 Journal Article
%A Leonid Golinskii
%T Absolutely continuous measures on the unit circle with sparse Verblunsky coefficients
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2004
%P 408-420
%V 11
%N 4
%U http://geodesic.mathdoc.fr/item/JMAG_2004_11_4_a2/
%G en
%F JMAG_2004_11_4_a2
Orthogonal polynomials and measures on the unit circle are fully determined by their Verblunsky coefficients through the Szegő recurrences. We study measures $\mu$ from the Szegő class whose Verblunsky coefficients vanish off a sequence of positive integers with exponentially growing gaps. All such measures turn out to be absolutely continuous on the circle. We also gather some information about the density function $\mu'$.
