A formula related to CMV matrices and Szego cocycles
Fengpeng Wang
TL;DR
This paper establishes a new formula linking transfer matrices and Dirichlet determinants specifically for CMV matrices, filling a notable gap in the spectral theory of these operators.
Contribution
It introduces the first analog of the Schrödinger operator formula for CMV matrices, advancing the understanding of their spectral properties.
Findings
Derived a formula connecting transfer matrices and Dirichlet determinants for CMV matrices
Bridged a gap in the spectral theory of CMV matrices
Enhanced tools for analyzing spectral properties of CMV operators
Abstract
For Schrodinger operators, there is a well known and widely used formula connecting the transfer matrices and Dirichlet determinants. No analog of this formula was previously known for CMV matrices. In this paper we fill this gap and provide the CMV analog of this formula.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Matrix Theory and Algorithms · Lanthanide and Transition Metal Complexes