Geodesic
Absolutely continuous measures on the unit circle with sparse Verblunsky coefficients
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2004), pp. 408-420.

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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 $\mu'$. 
@article{JMAG_2004_11_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},
     publisher = {mathdoc},
     volume = {11},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2004_11_a2/}
}
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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), pp. 408-420. http://geodesic.mathdoc.fr/item/JMAG_2004_11_a2/