Cantor polynomials and some related classes of OPRL

Abstract

We explore the spectral theory of the orthogonal polynomials associated to the classical Cantor measure and similar singular continuous measures. We prove regularity in the sense of Stahl–Totik with polynomial bounds on the transfer matrix. We present numerical evidence that the Jacobi parameters for this problem are asymptotically almost periodic and discuss the possible meaning of the isospectral torus and the Szegő class in this context.

Additional Information

© 2014 Elsevier Inc. Received 30 December 2013; received in revised form 5 March 2014; accepted 7 April 2014; Available online 16 April 2014. The first author was supported by the Simons Foundation as a Simons Postodoctal Fellow. The second author was supported in part by National Science Foundation grants DMS-0968856; 1265592.

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