On a Domain Equivalent to the Bidisk.
On a Minimal Complex Norm that Extends the Real Euclidean Norm.
On a minimum principle in several complex variables
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 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 Bergman completeness of pseudoconvex Reinhardt domains
On derived and integrated sets of basic sets of polynomials of several complex variables.
On holomorphic isometries for the Kobayashi and Carathéodory distances on complex manifolds
It is shown that under certain conditions every holomorphic isometry for the Carathéodory or the Kobayashi distances is an isometry for the corrisponding metrics. These results are used to give a characterization of biholomorphic mappings between convex domains and complete circular domains.
On holomorphic maps between domains in
On matrix Reinhardt domains.
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 the automorphisms of circular and Reinhardt domains in complex Banach spaces.
On the differential properties of Temlyakov-type and Temlyakov-Bavrin-type integrals.
On the Forelli-Rudin construction and weighted Bergman projections
On the Fourier-Laplace representation of analytic functions in tube domains.
On the Holomorphic Endomorphisms of the Ball
Sia un endomorfismo olomorfo della palla unitaria aperta di . In questa nota proviamo che certe ipotesi minimali, relative al comportamento di su un orociclo e vicino ad un punto del bordo, assicurano che è un automorfismo olomorfo di .
On the Mapping Problem for Algebraic Real Hypersurfaces.
On the Phragmén-Lindelöf principle for a polyangle
On the spectrum of A(Ω) and
We study some properties of the maximal ideal space of the bounded holomorphic functions in several variables. Two examples of bounded balanced domains are introduced, both having non-trivial maximal ideals.
On the zero set of the Kobayashi-Royden pseudometric of the spectral unit ball
Given A∈ Ωₙ, the n²-dimensional spectral unit ball, we show that if B is an n×n complex matrix, then B is a “generalized” tangent vector at A to an entire curve in Ωₙ if and only if B is in the tangent cone to the isospectral variety at A. In the case of Ω₃, the zero set of the Kobayashi-Royden pseudometric is completely described.