Analytic smoothing effect for nonlinear Schrِdinger equation with quintic nonlinearity

We prove the global existence of analytic solutions to nonlinear Schrödinger equation with quintic nonlinearity in n space dimensions for sufficiently small Cauchy data with exponential decay. The smallness assumption on the data is imposed in terms of the critical Sobolev space H ˙ n / 2 − 1 / 2 . Moreover, a characterization of some class of analytic functions is given.