Session S30 - Mathematical Methods in Quantum Mechanics

Thursday, July 15, 17:30 ~ 18:10 UTC-3

Dispersive Estimates for Schrödinger Equations

Ricardo Weder

Universidad Nacional Autónoma de México, Mexico   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The importance of the dispersive estimates for Schrödinger equations in spectral theory and in nonlinear analysis will be discussed. Furthermore, the literature on the Lp − Lp′ estimates will be reviewed, starting with the early results in the 1990 th, and with an emphasis in the results in one dimension. New results will be presented, in Lp − Lp′ estimates for matrix Schrödinger equations in the half-line, with general selfadjoint boundary condition, and in matrix Schrödinger equations in the full-line with point interactions. In both cases we consider integrable matrix potentials that have a finite first moment.

References

[1] T. Aktosun and R. Weder, Direct and Inverse Scattering for the Matrix Schrödinger Equation, Applied Mathematical Sciences 203 , Springer Verlag, New York, 2021.

[2] I. Naumkin, R. Weder, Lp − Lp′ estimates for matrix Schrödinger equations, Journal of Evolution Equations, online first https://doi.org/10.1007/s00028- 020-00605-x, (2020).

View abstract PDF