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It is known that a real analytic CR function f on a real analytic, genericsubmanifold M in C^N can be holomorphically extended. A stronger result on afinite type, real analytic, generic submanifold M is found in which we assume fa continuous CR function with real analytic imaginary part Im(f). The idea iscontained in a general Schwarz Reflection Principle in one complex variable.

An extension result of CR Functions by a general Schwarz reflection principle