basque center for applied mathematics

## Eceizabarrena, Daniel

• ### The Pointwise Convergence of the Solution to the Schrödinger Equation

Date:
27-06-2016
University:
Country:
Spain
File:
The present document corresponds to the subject Trabajo Fin de Máster being part of the Master's Degree in Mathematics and Applications at Universidad Autónoma de Madrid. The objective of this dissertation is to analyse the almost everywhere convergence of the solution to the Schrödinger equation to the given initial data.

This problem was presented by Lennart Carleson in 1980, when he proved convergence for the one space dimensional problem and for data lying in Sobolev spaces Hs with exponents $s \ge 1/4$. Since then, many partial results have shown that Sobolev spaces are the convenient setup to work with. The problem was solved in one dimension in 1981 by B.E.J. Dahlberg and C.E. Kenig, who showed Carleson's condition was also necessary. We review both results in the first chapter.

The question still remains unsolved for higher dimensions. Throughout the rest of the chapters, we present several partial results, particularly the best necessary and sufficient conditions known so far.

• ### Distribution Theory and Fundamental Solutions of Differential Operators

Date:
24-06-2015
University:
Euskal Herriko Unibertsitatea (UPV/EHU)
Country:
Spain
File: