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.
The essential norm of the generalized Hankel operators on the Bergman space of the unit ball in .
The essential norms of composition operators between generalized Bloch spaces in the polydisc and their applications.
The exceptional sets for functions from the Bergman space
The existence and the continuation of holomorphic solutions for convolution equations in tube domains
The extended future tube conjecture for SO(1, )
Let be the open upper light cone in with respect to the Lorentz product. The connected linear Lorentz group acts on and therefore diagonally on the -fold product where We prove that the extended future tube is a domain of holomorphy.
The field of Nash functions and factorization of polynomials
The algebraically closed field of Nash functions is introduced. It is shown that this field is an algebraic closure of the field of rational functions in several variables. We give conditions for the irreducibility of polynomials with Nash coefficients, a description of factors of a polynomial over the field of Nash functions and a theorem on continuity of factors.
The fundamental group at infinity of affine surfaces.
The Gleason problem for , , .
The Hölder continuity of the Bergman projection and proper holomorphic mappings
The holomorphic automorphism group of the complex disk.