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arXiv · 1709.05986

The wedge-of-the-edge theorem: edge-of-the-wedge type phenomenon within the common real boundary

J. E. Pascoe
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Abstract

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 $\mathbb{C}^d$ with all coordinates in the upper and lower half planes respectively, through a set in real space, $\mathbb{R}^d.$ 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 $\mathbb{R}^d$ which 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.

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J. E. Pascoe. 2017-09-18. The wedge-of-the-edge theorem: edge-of-the-wedge type phenomenon within the common real boundary. https://arxiv.org/abs/1709.05986

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