On a Class of Verblunsky Parameters that Corresponds to Guseinov's Class of Jacobi Parameters

摘要

The direct and inverse Geronimus relations between Verblunsky parame- ters of measures on the unit circle and Jacobi parameters of their Szego? trans forms have been used to prove that Guseinov's class of Jacobi parameters (|an-1|+|bn|) < 8 is in a canonical correspondence with the following class of Verblunsky parameters an ? 0 and |an+2 - an| < 8.