A Blow-up Approach to Edge-of-the-Wedge Theorems
The Edge-of-the-Wedge Theorem is a result about extension of holomorphic
functions of several complex variables. Even in one variable the result is
of interest. A particularly nice partial differential equations proof of
this result in one variable will be sketched, based on the view of a
holomorphic function as a solution of the Cauchy-Riemann equations. It
will be shown that this same sort of proof can be extended to the higher
dimensional case using the notions of a (real) blow-up and of involutive
and hypoanalytic structures. These are structures on a manifold which may
be viewed as generalizations of CR and complex structures. Generalizations
of the classical edge-of-the-wedge theorem to the setting where the base
manifold itself has a hypoanalytic structure rather than a complex
structure will be discussed. This includes in particular new versions of
the edge-of-the-wedge theorem on CR manifolds.
Back to
Spring 1997 meeting of the PNGS.
Suggestions or corrections to
Jack Lee <lee@math.washington.edu>.