On moduli of boundary values of holomorphic functions.
On Nevanlinna's second main theorem in projective space.
On non-isomorphism of Banach spaces of holomorphic functions
On -th order of a function of two complex variables analytic in the unit polydisc
On pluriharmonic interpolation.
On Pólya's Theorem in several complex variables
Let K be a compact set in ℂ, f a function analytic in ℂ̅∖K vanishing at ∞. Let be its Taylor expansion at ∞, and the sequence of Hankel determinants. The classical Pólya inequality says that , where d(K) is the transfinite diameter of K. Goluzin has shown that for some class of compacta this inequality is sharp. We provide here a sharpness result for the multivariate analog of Pólya’s inequality, considered by the second author in Math. USSR Sbornik 25 (1975), 350-364.
On Polynomials and Exponential Polynomials in Several Complex Variables.
On polynomials whose fibres are irreducible with no critical points.
On propagation of boundary continuity of holomorphic functions of several variables
We prove that continuity properties of bounded analytic functions in bounded smoothly bounded pseudoconvex domains in two-dimensional affine space are determined by their behaviour near the Shilov boundary. Namely, if the function has continuous extension to an open subset of the boundary containing the Shilov boundary it extends continuously to the whole boundary. If it is e.g. Hölder continuous on such a boundary set, it is Hölder continuous on the closure of the domain. The statements may fail...
On rational approximation in a ball in .
On roots of the automorphism group of a circular domain in
We study the properties of the group Aut(D) of all biholomorphic transformations of a bounded circular domain D in containing the origin. We characterize the set of all possible roots for the Lie algebra of Aut(D). There exists an n-element set P such that any root is of the form α or -α or α-β for suitable α,β ∈ P.
On self-commutators of Toeplitz operators with rational symbols
We prove that the self-commutator of a Toeplitz operator with unbounded analytic rational symbol has a dense domain in both the Bergman space and the Hardy space of the unit disc. This is a basic step towards establishing whether the self-commutator has a compact or trace-class extension.
On series of homogeneous polynomials and their partial sums
On some characterizations of Carleson type measure in the unit ball.
On some generalizations of Jacobi's residue formula
On some inequalities in holomorphic function theory in polydisk related to diagonal mapping
We present a description of the diagonal of several spaces in the polydisk. We also generalize some previously known contentions and obtain some new assertions on the diagonal map using maximal functions and vector valued embedding theorems, and integral representations based on finite Blaschke products. All our results were previously known in the unit disk.
On some new embedding theorems for some analytic classes in the unit ball.
On Some of Professor Peter Rusev's Contributions
MSC 2010: 33-00, 33C45, 33C52, 30C15, 30D20, 32A17, 32H02, 44A05The 6th International Conference "Transform Methods and Special Functions' 2011", 20 - 23 October 2011 was dedicated to the 80th anniversary of Professor Peter Rusev, as one of the founders of this series of international meetings in Bulgaria, since 1994. It is a pleasure to congratulate the Jubiliar on behalf of the Local Organizing Committee and International Steering Committee, and to present shortly some of his life achievements...
On some properties of a differential operator on the polydisk.
On some properties of holomorphic spaces based on Bergman metric ball and Luzin area operator.