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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...

Global time estimates for solutions to equations of dissipative type

Michael Ruzhansky, James Smith (2005)

Journées Équations aux dérivées partielles

Global time estimates of L p - L q norms of solutions to general strictly hyperbolic partial differential equations are considered. The case of special interest in this paper are equations exhibiting the dissipative behaviour. Results are applied to discuss time decay estimates for Fokker-Planck equations and for wave type equations with negative mass.

Graphs with multiple sheeted pluripolar hulls

Evgeny Poletsky, Jan Wiegerinck (2006)

Annales Polonici Mathematici

We study the pluripolar hulls of analytic sets. In particular, we show that hulls of graphs of analytic functions can be multiple sheeted and sheets can be separated by a set of zero dimension.

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