三次晶格上拉普拉斯算子的加权估计

IF 0.8 4区数学 Q2 MATHEMATICS

Arkiv for Matematik Pub Date : 2019-01-01 DOI:10.4310/arkiv.2019.v57.n2.a8

E. Korotyaev, J. S. Møller

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引用次数: 9

摘要

我们考虑立方晶格Zd上的离散拉普拉斯算子Δ，并推导出对群eitΔ和解(Δ−z)−1的估计，并对合适的q 2用q(Zd)加权。我们将得到的结果应用于三维离散的Schrödinger算子，这些算子具有p(Zd)的势，具有合适的p1。

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Weighted estimates for the Laplacian on the cubic lattice

We consider the discrete Laplacian Δ on the cubic lattice Zd, and deduce estimates on the group eitΔ and the resolvent (Δ−z)−1, weighted by q(Zd)-weights for suitable q 2. We apply the obtained results to discrete Schrödinger operators in dimension d 3 with potentials from p(Zd) with suitable p 1.

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来源期刊

Arkiv for Matematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishing research papers, of short to moderate length, in all fields of mathematics.