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

Germs of holomorphic mappings between real algebraic hypersurfaces

Nordine Mir (1998)

Annales de l'institut Fourier

We study germs of holomorphic mappings between general algebraic hypersurfaces. Our main result is the following. If ( M , p 0 ) and ( M ' , p 0 ' ) are two germs of real algebraic hypersurfaces in N + 1 , N 1 , M is not Levi-flat and H is a germ at p 0 of a holomorphic mapping such that H ( M ) M ' and Jac ( H ) 0 then the so-called reflection function associated to H is always holomorphic algebraic. As a consequence, we obtain that if M ' is given in the so-called normal form, the transversal component of H is always algebraic. Another corollary of...

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