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Conical Fourier-Borel transformations for harmonic functionals on the Lie ball

Mitsuo Morimoto, Keiko Fujita (1996)

Banach Center Publications

Let L(z) be the Lie norm on ˜ = n + 1 and L*(z) the dual Lie norm. We denote by Δ ( B ˜ ( R ) ) the space of complex harmonic functions on the open Lie ball B ˜ ( R ) and by E x p Δ ( ˜ ; ( A , L * ) ) the space of entire harmonic functions of exponential type (A,L*). A continuous linear functional on these spaces will be called a harmonic functional or an entire harmonic functional. We shall study the conical Fourier-Borel transformations on the spaces of harmonic functionals or entire harmonic functionals.

Connected components of the strata of the moduli spaces of quadratic differentials

Erwan Lanneau (2008)

Annales scientifiques de l'École Normale Supérieure

In two fundamental classical papers, Masur [14] and Veech [21] have independently proved that the Teichmüller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore interesting to have a classification of the ergodic components. Veech has proved that these strata are not necessarily connected. In a recent work [8], Kontsevich and Zorich have completely classified the components in the particular case where the quadratic...

Constructing blow-analytic isomorphisms

Toshizumi Fukui, Tzee-Char Kuo, Laurentiu Paunescu (2001)

Annales de l’institut Fourier

In this paper we construct non-trivial examples of blow-analytic isomorphisms and we obtain, via toric modifications, an inverse function theorem in this category. We also show that any analytic curve in n , n 3 , can be deformed via a rational blow- analytic isomorphism of n , to a smooth analytic arc.

Construction d’hypersurfaces irréductibles avec lieu singulier donné dans n

Jean-Pierre Demailly (1980)

Annales de l'institut Fourier

Étant donné un ensemble analytique S de codimension 2 dans C n , nous construisons des hypersurfaces irréductibles de lieu singulier S , avec contrôle de la croissance. À partir d’un contre-exemple au problème de Bezout transcendant, dû à M. Cornalba et B. Shiffman, nous montrons l’existence d’une courbe irréductible d’ordre 0 dans C 2 , dont le lieu singulier est d’ordre infini. Nous étudions également en application certaines propriétés arithmétiques de l’anneau de convolution ' ( R n ) .

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