Weighted estimates for the Laplacian on the cubic lattice

Evgeny Korotyaev; Jacob Schach Møller

doi:10.4310/ARKIV.2019.v57.n2.a8

Weighted estimates for the Laplacian on the cubic lattice

Department of Mathematics

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Abstract

We consider the discrete Laplacian Δ on the cubic lattice Z ^d, and deduce estimates on the group e ^itΔ and the resolvent (Δ−z) ⁻¹,weightedbyℓ ^q (Z ^d)-weights for suitable q≥2. We apply the obtained results to discrete Schrödinger operators in dimension d≥3 with potentials from ℓ ^p(Z ^d) with suitable p≥1.

Original language	English
Journal	Arkiv foer Matematik
Volume	57
Issue	2
Pages (from-to)	397-428
Number of pages	32
ISSN	0004-2080
DOIs	https://doi.org/10.4310/ARKIV.2019.v57.n2.a8
Publication status	Published - 2019

Keywords

Bessel function
Birman-Schwinger
Resolvent
discrete Laplacian

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title = "Weighted estimates for the Laplacian on the cubic lattice",

abstract = "We consider the discrete Laplacian Δ on the cubic lattice Z d, and deduce estimates on the group e itΔ and the resolvent (Δ−z) −1,weightedbyℓ q (Z d)-weights for suitable q≥2. We apply the obtained results to discrete Schr{\"o}dinger operators in dimension d≥3 with potentials from ℓ p(Z d) with suitable p≥1.",

keywords = "Bessel function, Birman-Schwinger, Resolvent, discrete Laplacian",

author = "Evgeny Korotyaev and M{\o}ller, {Jacob Schach}",

year = "2019",

doi = "10.4310/ARKIV.2019.v57.n2.a8",

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T1 - Weighted estimates for the Laplacian on the cubic lattice

AU - Korotyaev, Evgeny

AU - Møller, Jacob Schach

PY - 2019

Y1 - 2019

N2 - We consider the discrete Laplacian Δ on the cubic lattice Z d, and deduce estimates on the group e itΔ and the resolvent (Δ−z) −1,weightedbyℓ q (Z d)-weights for suitable q≥2. We apply the obtained results to discrete Schrödinger operators in dimension d≥3 with potentials from ℓ p(Z d) with suitable p≥1.

AB - We consider the discrete Laplacian Δ on the cubic lattice Z d, and deduce estimates on the group e itΔ and the resolvent (Δ−z) −1,weightedbyℓ q (Z d)-weights for suitable q≥2. We apply the obtained results to discrete Schrödinger operators in dimension d≥3 with potentials from ℓ p(Z d) with suitable p≥1.

KW - Bessel function

KW - Birman-Schwinger

KW - Resolvent

KW - discrete Laplacian

UR - http://www.scopus.com/inward/record.url?scp=85074108166&partnerID=8YFLogxK

U2 - 10.4310/ARKIV.2019.v57.n2.a8

DO - 10.4310/ARKIV.2019.v57.n2.a8

M3 - Journal article

SN - 0004-2080

VL - 57

SP - 397

EP - 428

JO - Arkiv foer Matematik

JF - Arkiv foer Matematik

IS - 2

ER -

Weighted estimates for the Laplacian on the cubic lattice

Abstract

Keywords

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