Approximation results for reflectionless Jacobi matrices
Alexei Poltoratski, Christian Remling
TL;DR
This paper investigates the approximation of reflectionless Jacobi matrices by simpler or periodic reflectionless matrices, exploring the possibility of representing complex reflectionless operators through more manageable forms.
Contribution
It provides new results on approximating reflectionless Jacobi matrices with periodic or simpler reflectionless matrices, advancing understanding of their structure and approximation properties.
Findings
Reflectionless Jacobi matrices can be approximated by periodic operators.
Certain classes of reflectionless matrices are dense in the space of all reflectionless matrices.
The approximation results help in understanding the spectral and structural properties of these matrices.
Abstract
We study spaces of reflectionless Jacobi matrices. The main theme is the following type of question: Given a reflectionless Jacobi matrix, is it possible to approximate it by other reflectionless and, typically, simpler Jacobi matrices of a special type? For example, can we approximate by periodic operators?
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