Weighted estimates for the Laplacian on the cubic lattice

Evgeny L. Korotyaev Saint Petersburg State University Jacob Schach Møller Aarhus University

Mathematical Physics mathscidoc:1912.43044

Arkiv for Matematik, 57, (2), 397-428, 2019
We consider the discrete Laplacian $\Delta$ on the cubic lattice $\mathbb{Z}^d$, and deduce estimates on the group $e^{i t \Delta}$ and the resolvent $(\Delta-z)^{-1}$, weighted by $\ell^q (\mathbb{Z}^d)$-weights for suitable $q \geqslant 2$. We apply the obtained results to discrete Schrödinger operators in dimension $d \geqslant 3$ with potentials from $\ell^p (\mathbb{Z}^d)$ with suitable $p \geqslant1$.
discrete Laplacian, resolvent, Bessel function, Birman–Schwinger
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@inproceedings{evgeny2019weighted,
  title={Weighted estimates for the Laplacian on the cubic lattice},
  author={Evgeny L. Korotyaev, and Jacob Schach Møller},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204141844691005600},
  booktitle={Arkiv for Matematik},
  volume={57},
  number={2},
  pages={397-428},
  year={2019},
}
Evgeny L. Korotyaev, and Jacob Schach Møller. Weighted estimates for the Laplacian on the cubic lattice. 2019. Vol. 57. In Arkiv for Matematik. pp.397-428. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204141844691005600.
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