Regularity and the Cesàro–Nevai class

Creators: Simon, Barry

Abstract

We consider OPRL and OPUC with measures regular in the sense of Ullman–Stahl–Totik and prove consequences on the Jacobi parameters or Verblunsky coefficients. For example, regularity on [−2,2] implies lim_(N→∞)N^(-1)[∑_(n=1)^N(a_n-1)^2 + b_n^2] = 0.

Additional Information

© 2008 Elsevier Inc. Received 23 October 2007; revised 28 February 2008; accepted 10 April 2008. Communicated by Leonid Golinskii. Available online 31 October 2008. The research was supported in part by NSF grants DMS-0140592 and DMS-0652919.

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