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.
The holomorphic automorphism groups of twisted Fock-Bargmann-Hartogs domains
We consider a certain class of unbounded nonhyperbolic Reinhardt domains which is called the twisted Fock-Bargmann-Hartogs domains. By showing Cartan's linearity theorem for our unbounded nonhyperbolic domains, we give a complete description of the automorphism groups of twisted Fock-Bargmann-Hartogs domains.
The homogeneous transfinite diameter of a compact subset of
Let K be a compact subset of . A sequence of nonnegative numbers defined by means of extremal points of K with respect to homogeneous polynomials is proved to be convergent. Its limit is called the homogeneous transfinite diameter of K. A few properties of this diameter are given and its value for some compact subsets of is computed.
The Hua system on irreducible Hermitian symmetric spaces of nontube type
Let be an irreducible Hermitian symmetric space of noncompact type. We study a - invariant system of differential operators on called the Hua system. It was proved by K. Johnson and A. Korányi that if is a Hermitian symmetric space of tube type, then the space of Poisson-Szegö integrals is precisely the space of zeros of the Hua system. N. Berline and M. Vergne raised the question about the nature of the common solutions of the Hua system for Hermitian symmetric spaces of nontube type. In...
The ideal boundary of a domain in
The interpolation theorem for holomorphic generalized functions
The Iversen theorem in a polydisc.
The Jacobian conjecture and the extensions of polynomial embeddings.
The Lindelöf principle in ℂn
Let D be a bounded domain in ℂn. A holomorphic function f: D → ℂ is called normal function if f satisfies a Lipschitz condition with respect to the Kobayashi metric on D and the spherical metric on the Riemann sphere ̅ℂ. We formulate and prove a few Lindelöf principles in the function theory of several complex variables.
The linear fractional model on the ball.
The Local Hull of Holomorphy of a Surface in the Space of Two Complex Variables.