The Bergman kernel of the minimal ball and applications
In this note we compute the Bergman kernel of the unit ball with respect to the smallest norm in that extends the euclidean norm in and give some applications.
The Bergman kernel on certain weakly pseudoconvex domains.
The Bergman Kernel on Uniformly Extendable Pseudoconvex Domains.
The Bergman projection in spaces of entire functions
We establish -estimates for the weighted Bergman projection on a nonsingular cone. We apply these results to the weighted Fock space with respect to the minimal norm in ℂⁿ.
The Bergman projection on harmonic functions
The Bergmann Kernel and Biholomorphic Mappings of Pseudokonvex Domains.
The Bloch space for the minimal ball
We introduce the Bloch space for the minimal ball and we prove that this space can be identified with the dual of a certain analytic space which is strongly related to the Bergman theory on the minimal ball.
The Bloch Space of M-Harmonic Functions on Bounded Symmetric Domains.
The canonical solution operator to aDOb∂aFOb restricted to spaces of entire functions
The Cartan-Thullen theorem for Banach spaces
The Cauchy kernel for cones
A new representation of the Cauchy kernel for an arbitrary acute convex cone Γ in ℝⁿ is found. The domain of holomorphy of is described. An estimation of the growth of near the singularities is given.
The Cauchy transform of continuous linear functionals and projections on the weighted spaces of analytic functions.
The class of holomorphic functions representable by Carleman formula
The classical and the modified Neumann problems for the inhomogeneous pluriholomorphic system in polydiscs.
The corona theorem for the ball and polydisc.
The diagonal mapping in mixed norm spaces
For any holomorphic function F in the unit polydisc Uⁿ of ℂⁿ, we consider its restriction to the diagonal, i.e., the function in the unit disc U of ℂ defined by F(z) = F(z,...,z), and prove that the diagonal mapping maps the mixed norm space of the polydisc onto the mixed norm space of the unit disc for any 0 < p < ∞ and 0 < q ≤ ∞.
The differential equation y' = fy in the algebras H(D).
The distribution of extremal points for Kergin interpolations : real case
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....
The effect of rational maps on polynomial maps
We describe the polynomials P ∈ ℂ[x,y] such that . As applications we give new examples of bad field generators and examples of families of polynomials with smooth and irreducible fibers.
The Ekeland's variational principle for vector-valued multifunctions.