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Continuation of holomorphic solutions to convolution equations in complex domains

Ryuichi Ishimura; Jun-ichi Okada; Yasunori Okada — 2000

Annales Polonici Mathematici

For an analytic functional $S$ on $ℂ^{n}$ , we study the homogeneous convolution equation S * f = 0 with the holomorphic function f defined on an open set in $ℂ^{n}$ . We determine the directions in which every solution can be continued analytically, by using the characteristic set.

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