Absolutely continuous measures on the unit circle with sparse Verblunsky coefficients

  • Leonid Golinskii

Анотація

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 $\mu'$.

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(1)
Golinskii, L. Absolutely continuous measures on the unit circle with sparse Verblunsky coefficients. Мат. физ. анал. геом. 2004, 11, 408-420.

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