# Семинар 25 февраля

### Доклад Е.Л. Коротяева «Estimates for Laplacians on the cubic lattice».

#### Аннотация

We consider the Laplacian $$D$$ on the lattice $$Z^d, d\ge 3$$ and estimate the group $$e^{itD}$$ and the resolvent $$(D-l)^{-1}$$ in the weighted spaces. The proof of the resolvent estimates is based on the investigation of the kernel of the resolvent. We obtain the estimate of the kernel of the resolvent $$(D-l)^{-1}$$ and their Hölder type estimates. We apply the obtained results to Schrödinger operators. In particular, in the case $$d\ge 5$$ Schrödinger operators with potential $$V\in \ell^p(Z^d)$$ has only finite number of eigenvalues and there is no singular-continuous spectrum. It is the joint result with Jacob  Schach  Moller.