On the spectral properties of discrete Schrödinger operators

Monvel, Anne Boutet de; Sahbani, Jaouad

doi:10.1016/s0764-4442(98)80078-5

Cited by 32 publications

(47 citation statements)

References 4 publications

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“…For closely related problems, we mention that the results of Sahbani and Boutet de Monvel [2], were recently extended to general lattices by Parra and Richard [19]. In addition, the result in [7], on absence of embedded eigenvalues (away from {−d, d}) for finitely supported potentials, has a generalization to other lattices in [1,Thm.…”

Section: Introduction and Main Resultsmentioning

confidence: 84%

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Weighted estimates for the Laplacian on the cubic lattice

Møller

2019

Arkiv För Matematik

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Section: Introduction and Main Resultsmentioning

confidence: 84%

“…The claim in (d) that σ pp (H) is finite under the assumed conditions, follows by combining Lemma 4.3 with Lemma 4.7, keeping in mind Remark 1.4 (2). The lemma implies that σ BS (H) is a finite set.…”

Section: Schrödinger Operatorsmentioning

confidence: 80%

Weighted estimates for the Laplacian on the cubic lattice

Møller

2019

Arkiv För Matematik

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“…Then g ∈ L 1 ((1, ∞)) 3. a n is a bounded sequence of non-negative numbers which are non-zero on an infinite subset of Z ν+1 + . 4. Let g(R) = a n χ {n∈Z ν :|n i |>R, ∀1≤i≤ν+1} .…”

Section: µ Is Absolutely Continuousmentioning

confidence: 99%

“…and let a n be a sequence satisfying the Hypothesis 2.3(3)- (4). Then there is a critical energy e(µ) > e 0 such that…”

Section: Letmentioning

confidence: 99%

Spectra of Anderson type models with decaying randomness

Krishna

Sinha

2001

Proc. Math. Sci.

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In this paper we consider some Anderson type models, with free parts having long range tails and with the random perturbations decaying at different rates in different directions and prove that there is a.c. spectrum in the model which is pure. In addition, we show that there is pure point spectrum outside some interval. Our models include potentials decaying in all directions in which case absence of singular continuous spectrum is also shown.

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“…These results first appeared in [2]. Independent work on the commutator method for the graph Z n has appeared in [6] and [7].…”

Section: Introductionmentioning

confidence: 96%