## IMA Postdoc Seminar (March 02, 2010)

**Speaker:** Shao, Shuanglin (IMA)

**Title: **Analyticity of extremals to the Airy Strichartz inequality.

**Abstract: **The Airy Strichartz inequality asserts that the linear operator, e^{-t
\partial_x3} f, is bounded from L^2 \to L^8_{t,x}. In this talk, we will
first prove the existence of extremals to this inequality by using the
linear profile decomposition; Moreover, we show that, if f is an extremal,
then f is exponentially decaying in the Fourier space so that f can be
extended to be an entire function on the complex domain. This is a joint
work with Dirk Hundertmark.