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7 papers
Typicality of operators on Fréchet algebras admitting a hypercyclic algebra
William Alexandre, Clifford Gilmore, Sophie Grivaux
This paper is devoted to the study of typical properties (in the Baire Category sense) of certain classes of continuous linear operators acting on Fréchet algebras, endowed with th…
Extension of holomorphic functions defined on singular complex hypersurfaces with growth estimates in strictly pseudoconvex domains of
William Alexandre, Emmanuel Mazzilli
Let be a strictly pseudoconvex domain and be a singular analytic set of pure dimension in such that and is transverse. We giv…
Zero Sets of H^p Functions in Convex Domains of Finite Type
William Alexandre
We give a condition under which a divisor X in a bounded convex domain of finite type D in C^n is the zero set of a function in a Hardy space H^p(D) for some p \textgreater{} 0. Th…
J-holomorphic discs and real analytic hypersurfaces
William Alexandre, Emmanuel Mazzilli
We give in \mathbb{R}^6 a real analytic almost complex structure J, a real analytic hypersurface M and a vector v in the Levi null set at 0 of M, such that there is no germ of J-ho…
Division of holomorphic functions and growth conditions
William Alexandre, Emmanuel Mazzilli
Let D be a strictly convex domain of C^n, f_1 and f_2 be two holomorphic functions defined on a neighborhood of closure of D and set X_l={z, f_l(z)=0}, l=1,2. Suppose that X_l\cap…
Extension with growth estimates of holomorphic functions defined on singular analytic spaces
William Alexandre, Emmanuel Mazzilli
Let D be a strictly convex domain and X be a singular analytic subset of C^2 such that the intersection of X and D is non empty. We give conditions under which a function holomophi…
A berndtsson-Andersson operator solving \bar\partial-equation with W^α-estimates on convex domains of finite type
William Alexandre
In this article, we use a Berndtsson-Andersson operator and the Bergman metric in order to solve the equation on convex domains of finite type for forms satisifying…