 Verblunsky's theorem states that any sequence of complex numbers in the open unit disk is the sequence of Verblunsky coefficients for a unique probability measure on the unit circle with infinite support.Geronimus's theorem states that the Verblunsky coefficients of the measure μ are the Schur parameters of the function formula_10 defined by the equations

Baxter's theorem states that the Verblunsky coefficients form an absolutely convergent series if and only if the moments of formula_1 form an absolutely convergent series and the weight function formula_13 is strictly positive everywhere.Szegő's theorem states that 
where formula_15 is the absolutely continuous part of the measure formula_1.