TY - JOUR
T1 - An inverse spectral problem for non-self-adjoint Jacobi matrices
AU - Pushnitski, Alexander
AU - Stampach, Frantisek
PY - 2023/12/8
Y1 - 2023/12/8
N2 - We consider the class of bounded symmetric Jacobi matrices J with positive off-diagonal elements and complex diagonal elements. With each matrix J from this class, we associate the spectral data, which consists of a pair (ν, ψ). Here ν is the spectral measure of |J| = √ J ∗J and ψ is a phase function on the real line satisfying |ψ| ≤ 1 almost everywhere with respect to the measure ν. Our main result is that the map from J to the pair (ν, ψ) is a bijection between our class of Jacobi matrices and the set of all spectral data.
AB - We consider the class of bounded symmetric Jacobi matrices J with positive off-diagonal elements and complex diagonal elements. With each matrix J from this class, we associate the spectral data, which consists of a pair (ν, ψ). Here ν is the spectral measure of |J| = √ J ∗J and ψ is a phase function on the real line satisfying |ψ| ≤ 1 almost everywhere with respect to the measure ν. Our main result is that the map from J to the pair (ν, ψ) is a bijection between our class of Jacobi matrices and the set of all spectral data.
M3 - Article
SN - 1073-7928
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
ER -