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Cauchy-Kowalewski extension theorems and representations of analytic functionals acting over special classes of real n-dimensional submanifolds of $C^{(} n + 1)$

Ryan, John (1984)

Proceedings of the 11th Winter School on Abstract Analysis

Cauchy-Riemann functions on manifolds of higher codimension in complex space.

M.S. Baouendi, L. Preiss Rothschild (1990)

Inventiones mathematicae

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.

Distribution des valeurs des fonctions analytiques multiformes

Bernard Aupetit, Abdelwahab Zraĭbi (1984)

Studia Mathematica

Extension of $C R$ -forms and related problems

Alessandro Perotti (1987)

Rendiconti del Seminario Matematico della Università di Padova

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 $ℂ^{N + 1}$ , $N \geq 1$ , $M$ is not Levi-flat and $H$ is a germ at $p_{0}$ of a holomorphic mapping such that $H (M) \subseteq M^{'}$ 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...