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Discrépance de la suite ( { n α } ) , α = ( 1 + 5 ) / 2

Yves Dupain — 1979

Annales de l'institut Fourier

Soit D * ( N ) la discrépance “à l’origine” de la suite n 1 + 5 2 . Nous montrons que lim sup D * ( N ) Log N = 3 20 Log 1 + 5 2 - 1 = 0 . 31 ⋯ , quantité inférieure à celle correspondant à la suite de van der Corput. Les techniques utilisées sont celles liées au développement en fraction continue.

Une estimation des coefficients tangents d'un courant positif fermé dans un domaine de C.

Philippe. Charpentier;  Yves Dupain — 1992

Publicacions Matemàtiques

In this paper, we study the behaviour near the boundary of the complex tangent coefficients of a closed positive current in a bounded domain of C with C boundary. Assuming that the current satisfies the Blaschke condition, we give a condition on the complex tangent coefficients which is better than the one which can be proved using the pseudo-distance introduced by A. Nagel, E. Stein and S. Wainger (in analogy with the case of domains in C). Moreover, when the domain is supposed to be pseudoconvex,...

Estimates for the Bergman and Szegö projections for pseudoconvex domains of finite type with locally diagonalizable Levi form.

Philippe Charpentier;  Yves Dupain — 2006

Publicacions Matemàtiques

In this paper, we give precise isotropic and non-isotropic estimates for the Bergman and Szegö projections of a bounded pseudoconvex domain whose boundary points are all of finite type and with locally diagonalizable Levi form. Additional local results on estimates of invariant metrics are also given.

Approximation par des fonctions holomorphes à croissance contrôlée.

Philippe Charpentier;  Yves Dupain;  Modi Mounkaila — 1994

Publicacions Matemàtiques

Let Ω be a bounded pseudo-convex domain in C with a C boundary, and let S be the set of strictly pseudo-convex points of ∂Ω. In this paper, we study the asymptotic behaviour of holomorphic functions along normals arising from points of S. We extend results obtained by M. Ortel and W. Schneider in the unit disc and those of A. Iordan and Y. Dupain in the unit ball of C. We establish the existence of holomorphic functions of given growth having a "prescribed behaviour" in almost all normals arising...

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