The Wedge-of-the-edge Theorem: Edge-of-the-wedge Type Phenomenon Within the Common Real Boundary

Pascoe, J. E.

Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 417-427

Résumé

The edge-of-the-wedge theorem in several complex variables gives the analytic continuation of functions defined on the poly upper half plane and the poly lower half plane, the set of points in $\mathbb{C}^{n}$ with all coordinates in the upper and lower half planes respectively, through a set in real space, $\mathbb{R}^{n}$. The geometry of the set in the real space can force the function to analytically continue within the boundary itself, which is qualified in our wedge-of-the-edge theorem. For example, if a function extends to the union of two cubes in $\mathbb{R}^{n}$ that are positively oriented with some small overlap, the functions must analytically continue to a neighborhood of that overlap of a fixed size not depending of the size of the overlap.

Détail

DOI : 10.4153/CMB-2018-025-3

Mots-clés : edge-of-the-wedge theorem, several complex variables, analytic continuation