Hadamard's multiplication theorem - recent developments
Harmonic extensions and the Böttcher-Silbermann conjecture
We present counterexamples to a conjecture of Böttcher and Silbermann on the asymptotic multiplicity of the Poisson kernel of the space and discuss conditions under which the Poisson kernel is asymptotically multiplicative.
H-holomorfne funkcije
Holomorphic series expansion of functions of Carleman type
Let f be a holomorphic function of Carleman type in a bounded convex domain D of the plane. We show that f can be expanded in a series f = ∑ₙfₙ, where fₙ is a holomorphic function in Dₙ satisfying for some constants C > 0 and 0 < ϱ < 1, and where (Dₙ)ₙ is a suitably chosen sequence of decreasing neighborhoods of the closure of D. Conversely, if f admits such an expansion then f is of Carleman type. The decrease of the sequence Dₙ characterizes the smoothness of f.
Holomorphically Closed Algebras of Analytic Functions.
Hypercyclicity of special operators on Hilbert function spaces
In this paper we give some sufficient conditions for the adjoint of a weighted composition operator on a Hilbert space of analytic functions to be hypercyclic.