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.

Коротяев Евгений Леонидович

профессор, доктор физико-математических наук

email:korotyaev@gmail.com

Fields of Research

• 1D inverse spectral theory for Schrodinger operator with periodic potentials, Sturm-Liouville problems on finite intervals, for the difference operators, Schrodinger operator with matrix-valued potentials, perturbed harmonic oscillator.
• Integrable systems (KdV and non-linear Schrodinger equation), a priori estimates for integrable systems, symplectic coordinates.
• Geometric function theory (harmonic and functional analysis, geometric function theory, the Lowner equation for the conformal mapping associated with quasimomentum)
• Scattering theory including few body systems in external fields.
• Schrodinger operators on periodic media, including graphs, and nano-media.
• Theory of resonances and inverse resonance scattering.
• Multidimensional inverse problems for Schrodinger operators on the lattice. Читать далее