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

  • J. E. Pascoe (a1)
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 $\mathbb{C}^{n}$ 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.

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Partially supported by National Science Foundation Mathematical Science Postdoctoral Research Fellowship DMS 1606260.

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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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