TL;DR
This paper investigates the asymptotic behavior and inverse problems of Jacobi matrices with lacunary spectral data, exploring their connections to canonical systems and de Branges spaces under certain growth conditions.
Contribution
It provides new asymptotic formulas and inverse results for Jacobi matrices with lacunary spectra, linking them to canonical systems and de Branges spaces.
Findings
Derived asymptotics of Jacobi matrix entries with lacunary spectra
Proved inverse spectral results for these matrices
Explored connections to canonical systems and de Branges spaces
Abstract
We find asymptotics of entries of Jacobi matrices with lacunary spectral data under some additional growth conditions. We also prove the inverse results. In addition, we study connections between Jacobi matrices, canonical systems and de Branges spaces for lacunary spectral data
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