On Rotated CMV Operators and Orthogonal Polynomials on the Unit Circle

Autor:	Ang, Ryan C. H.
Rok vydání:	2023
Předmět:	Mathematical Physics Mathematics - Classical Analysis and ODEs Primary 42C05 47A68 47B36 Secondary 81P45
Druh dokumentu:	Working Paper
DOI:	10.1080/10236198.2024.2348519
Popis:	Split-step quantum walk operators can be expressed as a generalised version of CMV operators with complex transmission coefficients, which we call rotated CMV operators. Following the idea of Cantero, Moral and Velazquez's original construction of the original CMV operators from the theory of orthogonal polynomials on the unit circle (OPUC), we show that rotated CMV operators can be constructed similarly via a rotated version of OPUCs with respect to the same measure, and admit an analogous LM-factorisation as the original CMV operators. We also develop the rotated second kind polynomials corresponding to the rotated OPUCs. We then use the LM-factorisation of rotated alternate CMV operators to compute the Gesztesy-Zinchenko transfer matrices for rotated CMV operators. Comment: 39 pages, 4 tables. Revised and accepted by Journal of Difference Equations and Applications
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.01423 Zobrazit plný text záznamu View this record from Arxiv