Dispersive equations

Dispersive equations

Table of Contents

1.	The Fourier transform of a complex Gaussian
2.	Solving the linear Schrödinger equation
3.	Bibliography

2. Solving the linear Schrödinger equation

2.1.	Well-posedness in Schwartz functions
2.2.	Well-posedness in tempered distributions
2.3.	Well-posedness on Sobolev space
2.4.	Explicit representation of the solution operator

2.2. Well-posedness in tempered distributions

←2.1. Well-posedness in Schwartz functions 2.3. Well-posedness on Sobolev space→

2.2. Well-posedness in tempered distributions🔗

By duality, we have that the solution operator defines a map 𝓢'(ℝ^n) → C(ℝ, 𝓢'(ℝ^n)).

←2.1. Well-posedness in Schwartz functions 2.3. Well-posedness on Sobolev space→