Cantor polynomials and some related classes of OPRL

JOURNAL OF APPROXIMATION THEORY

卷:191

Article

Krueger, Helge¹  Simon, Barry¹ 

[1] CALTECH, Pasadena, CA 91125 USA

关键词: Orthogonal polynomials;    Cantor set;    Almost periodic;   

DOI  :  10.1016/j.jat.2014.04.003

来源: Elsevier

【 摘 要 】

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 Szego class in this context. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free