On 3-graded Lie algebras, Jordan pairs and the canonical kernel function.
On a boundary version of Morera's theorem.
On a characterization of the analytic and meromorphic functions defined on some rigid domains
On a class of tangential Cauchy-Riemann maps
On a class of -equations without solutions
In this note we construct -equations (inhomogeneous Cauchy-Riemann equations) without solutions. The construction involves Bochner-Martinelli type kernels and differentiation with respect to certain parameters in appropriate directions.
On a Domain Equivalent to the Bidisk.
On a generalization of Fueter's theorem.
On a Minimal Complex Norm that Extends the Real Euclidean Norm.
On a minimum principle in several complex variables
On a new integral-type operator from the weighted Bergman space to the Bloch-type space on the unit ball.
On a space of smooth functions on a convex unbounded set in ℝn admitting holomorphic extension in ℂn
For some given logarithmically convex sequence M of positive numbers we construct a subspace of the space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in ℝn. Due to the conditions on M each function of this space admits a holomorphic extension in ℂn. In the current article, the space of holomorphic extensions is considered and Paley-Wiener type theorems are established. To prove these theorems, some auxiliary results on extensions of holomorphic functions...
On a two-variable zeta function for number fields
This paper studies a two-variable zeta function attached to an algebraic number field , introduced by van der Geer and Schoof, which is based on an analogue of the Riemann-Roch theorem for number fields using Arakelov divisors. When this function becomes the completed Dedekind zeta function of the field . The function is a meromorphic function of two complex variables with polar divisor , and it satisfies the functional equation . We consider the special case , where for this function...
On an Estimate of Axler and Shapiro.
On an integral formula of Berndtsson related to the inversion of the Fourier-Laplace transform of -closed -forms
We give a proof of an integral formula of Berndtsson which is related to the inversion of Fourier-Laplace transforms of -closed -forms in the complement of a compact convex set in .
On an integral operator on the unit ball in .
On an integral-type operator acting between Bloch-type spaces on the unit ball.
On an integral-type operator from Privalov spaces to Bloch-type spaces
Let H(B) denote the space of all holomorphic functions on the unit ball B of ℂⁿ. Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0. We study the integral-type operator , f ∈ H(B). The boundedness and compactness of from Privalov spaces to Bloch-type spaces and little Bloch-type spaces are studied
On an integral-type operator from Zygmund-type spaces to mixed-norm spaces on the unit ball.
On approximation by special analytic polyhedral pairs
For bounded logarithmically convex Reinhardt pairs "compact set - domain" (K,D) we solve positively the problem on simultaneous approximation of such a pair by a pair of special analytic polyhedra, generated by the same polynomial mapping f: D → ℂⁿ, n = dimΩ. This problem is closely connected with the problem of approximation of the pluripotential ω(D,K;z) by pluripotentials with a finite set of isolated logarithmic singularities ([23, 24]). The latter problem has been solved recently for arbitrary...
On approximation of analytic functions and generalized orders
A characterization of a generalized order of analytic functions of several complex variables by means of polynomial approximation and interpolation is established.