function decomposition on totally real submanifolds of
William S. Calbeck
Proc. Amer. Math. Soc. 117 (1993), 187-194
Primary 32A40; Secondary 32D99
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Abstract: For we show that functions defined on a totally real submanifold of can be locally decomposed into the sum of boundary values of holomorphic functions in wedges such that the boundary values are in .
The general case of a totally real submanifold is reduced to the flat case of in by an almost analytic change of variables. results in the flat case are then obtained using Fourier multipliers. In transporting these results back to the manifold we lose analyticity, so it is necessary to solve a problem in an appropriate domain. This gives holomorphy in the wedges but produces a error on the edge. This function is then holomorphically decomposed using the FBI transform with a careful analysis to check that the functions are up to the edge and do not destroy the behavior.
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