Spectral theory of a class of block Jacobi matrices and applications

Sahbani, Jaouad

doi:10.1016/j.jmaa.2016.01.078

Cited by 7 publications

(6 citation statements)

References 29 publications

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“…In [35] the case where h is a trigonometric polynomial symbol is studied and applications to different concrete models are given. Those applications represent additional motivations of our interest to this kind of operators.…”

Section: Notations and Main Resultsmentioning

confidence: 99%

Spectral and scattering theory for perturbed block Toeplitz operators

Cojuhari,

Sahbani

2017

Preprint

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We analyse spectral properties of a class of compact perturbations of block Toeplitz operators associated with analytic symbols. In particular, a limiting absorption principle and the absence of singular continuous spectrum are shown. The existence and the completeness of wave operators are also obtained. Our study is based on the construction of a conjugate operator in Mourre sense for the corresponding Laurent operators.

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Section: Notations and Main Resultsmentioning

confidence: 99%

Spectral and scattering theory for perturbed block Toeplitz operators

Cojuhari,

Sahbani

2017

Preprint

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“…In spite of having rV p , A p s ˝" 0 we cannot include periodic potentials as such because compactness remains a crucial assumption in our methods. For Mourre theory adapted for periodic potentials we refer to [GN] and [Sa2].…”

Section: Pd Hqmentioning

confidence: 99%

Bands of pure a.c. spectrum for lattice Schr{ö}dinger operators with a more general long range condition. Part I

Golenia,

Mandich

2021

Preprint

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Commutator methods are applied to get limiting absorption principles for the discrete standard and Molchanov-Vainberg Schrödinger operators, ∆`V and D`V on ℓ 2 pZ d q, with emphasis on d " 1, 2, 3. Considered are electric potentials V satisfying a long range condition of the type: V ´τ κ j V decays appropriately at infinity for some κ P N and all 1 ĺ j ĺ d, where τ κ j V is the potential shifted by κ units on the j th coordinate. More comprehensive results are obtained for small values of κ, e.g. κ " 1, 2, 3, 4. We work in a simplified framework in which the main takeaway appears to be the existence of bands where a limiting absorption principle holds, and hence pure absolutely continuous (a.c.) spectrum exists. Other decay conditions at infinity for V arise from an isomorphism between ∆ and D in dimension 2. Oscillating potentials are examples in application.

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“…In [14] we studied different classes of bounded self-adjoint block Jacobi operators given by (3.1) with applications to some concrete models. In this section we will focus on special unbounded cases.…”

Section: Block Jacobi Matricesmentioning

confidence: 99%