The Edge of the Wedge Theorem

The edge of the wedge theorem analyzes functions of n real variables which have some extension to holomorphic functions of n complex variables. The dimension n is crucial because it is th dimension of the set on whiich one gives Cauchy data for the Cauchy Riemann system. We shall examine other overdetermined systems of PDE. We shall also study subtles of the Cauchy problem e.g. what is the weakest way in which the CD is taken on. We shall also study the asymptotic CP thus answering a problem of Fefferman and Nirenberg.