Continuity of measures on the unit circle given by their reflection coefficients

L. B. Golinskii

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov

Abstract: Orthogonal polynomials on the unit circle are fully determined by their reflection coefficients through the Szegő recurrences. The discrete spectrum (the set of mass points) of measures is studied in terms of the reflection coefficients. The cases when these parameters go to zero or to nonzero complex number from the open unit disk are essentially different. New examples of singular continuous measures given by their reflection coefficients are presented.

Received: 05.02.2002

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