## 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.