25 февраля в 18:00 состоится заседание семинара кафедры Высшей математики и математической физики, ПОМИ (ауд. 106).

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.