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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 ℂ 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 boundary regularity for the p ⁢ a ⁢ r ⁢ t ⁢ i ⁢ a ⁢ l ¯ -equation on q -pseudo-convex domains

Heungju Ahn (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

For a bounded domain D of C n , we introduce a notion of « q -pseudoconvexity» of new type and prove that for a given ∂ ¯ -closed p , r -form f that is smooth up to the boundary on D , and for r ≥ q , there exists a p , r - 1 -form u smooth up to the boundary on D which is a solution of the equation ∂ ¯ ⁢ u = f

Global Parametrization of Scalar Holomorphic Coadjoint Orbits of a Quasi-Hermitian Lie Group

Benjamin Cahen (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Let G be a quasi-Hermitian Lie group with Lie algebra 𝔤 and K be a compactly embedded subgroup of G . Let ξ 0 be a regular element of 𝔤 * which is fixed by K . We give an explicit G -equivariant diffeomorphism from a complex domain onto the coadjoint orbit 𝒪 ( ξ 0 ) of ξ 0 . This generalizes a result of [B. Cahen, Berezin quantization and holomorphic representations, Rend. Sem. Mat. Univ. Padova, to appear] concerning the case where 𝒪 ( ξ 0 ) is associated with a unitary irreducible representation of G which is holomorphically...

Global problems on Nash functions.

Michel Coste, Jesús M. Ruiz, Masahiro Shiota (2004)

Revista Matemática Complutense

This is a survey on the history of and the solutions to the basic global problems on Nash functions, which have been only recently solved, namely: separation, extension, global equations, Artin-Mazur description and idempotency, also noetherianness. We discuss all of them in the various possible contexts, from manifolds over the reals to real spectra of arbitrary commutative rings.

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.

Currently displaying 61 – 80 of 105