2023/05/31 by Pushnitski, Alexander, Štampach, František · 1 citation
#47B36 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2305.19608
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.