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Seminar on Analysis, Differential Equations and Mathematical Physics
October 29, 2020 18:00, Rostov-on-Don, online

Dispersive Estimates for Schrödinger Equations

R. Weder

Instituto de Investigaciones en Matemáticas Aplicadas y Sistemas, Universidad Nacional Autónoma de México

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Abstract: The importance of the dispersive estimates for Schrödinger equations in spectral theory and in nonlinear analysis will be discussed. Furthermore, the literature on the $L^p-L^{p'}$ 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 $L^p-L^{p'}$ 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.

Language: English

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 (published in May 2020)
2. I. Naumkin, R. Weder, “$L^{p}-L^{p^{\prime}}$ estimates for matrix Schrödinger equations”, Journal of Evolution Equations, 2020, online first

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