## Abstract

In this chapter, we study smoothing properties of solutions of the initial value problem to the linear Schrödinger equation. In Section 4.1 we present general basic results related to solutions of the initial value problem. The global smoothing properties of solutions of the linear problem which are described by estimates of the type \(L^q(\mathbb{R}:L^p(\mathbb{R}^n))\) will be discussed in Section 4.2. In Section 4.3, we study the local smoothing arising from estimates of type \(L^2_{\text{loc}}(\mathbb{R}:H^{1/2}_{\text{loc}}(\mathbb{R}^n))\). We end the chapter with some remarks and comments regarding the issues discussed in the previous sections.

## Keywords

Unitary Group Initial Value Problem Decay Estimate Smoothing Effect Strichartz Estimate
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## Copyright information

© Springer-Verlag New York 2015