Singular Sets of Separately Analytic Functions

Saint Raymond [4] characterized singular sets of separately analytic functions of two real variables. The present author studies separately analytic functions of several vector variables. He proves that such functions are jointly analytic everywhere exept of a closed set S whose projections on some coordinate subspaces are pluripolar. For every closed set S with pluripolar projections there exists a separately analytic function whose domain of analyticity is the complement of S.

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