On the space of integral Dirichlet functions of several complex variables
We present an effective and elementary method of determining the topological type of a cuspidal plane curve singularity with given local parametrization.
On considère un polynôme , à coefficients réels non négatifs, à deux indéterminées. On montre que la connaissance des pôles des intégralesdonne des renseignements sur les racines du polynômes de Bernstein de . La détermination des pôles des intégrales peut se faire en utilisant certaines méthodes de Mellin. Des calculs explicites sont donnés.
Let be a non-pluripolar set in . Let be a function holomorphic in a connected open neighborhood of . Let be a sequence of polynomials with such thatWe show that ifwhere is a set in such that the global extremal function in , then the maximal domain of existence of is one-sheeted, andfor every compact set . If, moreover, the sequence is bounded then .If is a closed set in then if and only if each series of homogeneous polynomials , for which some subsequence ...
Soient un corps commutatif et un idéal de l’anneau des polynômes (éventuellement ). Nous prouvons une conjecture de C. Berenstein - A. Yger qui affirme que pour tout polynôme , élément de la clôture intégrale de l’idéal , on a une représentationoù .
We study extensions of classical theorems on gap power series of a complex variable to the multidimensional case.
Let be a holomorphic map from to defined in a neighborhood of zero such that If the jacobian determinant of is not identically zero, P. M. Eakin and G. A. Harris proved the following result: any formal power series such that is analytic is itself analytic. If the jacobian determinant of is identically zero, they proved that the previous conclusion is no more true. J. Chaumat and A.-M. Chollet extended this result in the case of formal power series satisfying growth conditions, of...
We show that a convex totally real compact set in admits an extremal array for Kergin interpolation if and only if it is a totally real ellipse. (An array is said to be extremal for when the corresponding sequence of Kergin interpolation polynomials converges uniformly (on ) to the interpolated function as soon as it is holomorphic on a neighborhood of .). Extremal arrays on these ellipses are characterized in terms of the distribution of the points and the rate of convergence is investigated....