Asymptotics and estimates for the discrete spectrum of the Schrödinger operator on a discrete periodic graph

Sloushch, V. A.

doi:10.1090/spmj/1635

Cited by 2 publications

(1 citation statement)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Korotyaev and Moller [52] discussed the spectral theory for potentials V ∈ ℓ p , p > 1. An upper bound on the number of discrete eigenvalues in terms of potentials was given by Korotyaev and Sloushch [56], Rozenblum and Solomyak [67]. Different types of trace formulas for Schrödinger operators on discrete periodic graphs are discussed in [45], [48], [53], [54].…”

Section: Historical Reviewmentioning

confidence: 99%

Inverse Problems for Finite Vector-Valued Jacobi Operators

Korotyaev

2019

Funct Anal Its Appl

View full text Add to dashboard Cite

We study resonances for Jacobi operators on the half lattice with matrix valued coefficient and finitely supported perturbations. We describe a forbidden domain, the geometry of resonances and their asymptotics when the main coefficient of the perturbation (determining its length of support) goes to zero. Moreover, we show that 1) Any sequence of points on the complex plane can be resonances for some Jacobi operators. In particular, the multiplicity of a resonance can be any number.2) The Jost determinant coincides with the Fredholm determinant up to the constant.3) The S-matrix on the a.c spectrum determines the perturbation uniquely. 5) The value of the Jost matrix at any finite sequence of points on the a.c spectrum determine the Jacobi matrix uniquely. The length of this sequence is equals to the upper point of the support perturbation.

show abstract