Zero sets and uniqueness sets of the classical Dirichlet space are not completely characterized yet. We define the concept of admissible functions for the Dirichlet space and then apply them to obtain a new class of zero sets for . Then we discuss the relation between the zero sets of and those of .
It is known that, under very general conditions, Blaschke products generate branched covering surfaces of the Riemann sphere. We are presenting here a method of finding fundamental domains of such coverings and we are studying the corresponding groups of covering transformations.
The aim of this paper is to consider the following three problems:i (1) for a given uniformly q-separated sequence satisfying certain conditions, find a coefficient function A(z) analytic in the unit disc such that f”’ + A(z)f = 0 possesses a solution having zeros precisely at the points of this sequence; (2) find necessary and sufficient conditions for the differential equation (*) in the unit disc to be Blaschke-oscillatory; (3) find sufficient conditions on the analytic coefficients of the...
This paper deals with an interpolation problem in the open unit disc of the complex plane. We characterize the sequences in a Stolz angle of , verifying that the bounded sequences are interpolated on them by a certain class of not bounded holomorphic functions on , but very close to the bounded ones. We prove that these interpolating sequences are also uniformly separated, as in the case of the interpolation by bounded holomorphic functions.
We present new sharp embedding theorems for mixed-norm analytic spaces in pseudoconvex domains with smooth boundary. New related sharp results in minimal bounded homogeneous domains in higher dimension are also provided. Last domains we consider are domains which are direct generalizations of the well-studied so-called bounded symmetric domains in Our results were known before only in the very particular case of domains of such type in the unit ball. As in the unit ball case, all our proofs are...
We construct an infinite uniform Frostman Blaschke product B such that B ∘ B is also a uniform Frostman Blaschke product. We also show that the set of uniform Frostman Blaschke products is open in the set of inner functions with the uniform norm.
We shall prove, using the result from our previous paper [Ann. Polon. Math. 88 (2006)], that for a quadratic polynomial mapping Q of ℝ² only the geometric shape of the critical set of Q determines whether the complexification of Q can be extended to an endomorphism of ℂℙ². At the end of the paper we describe some interesting classes of quadratic polynomial mappings of ℝ² and give some examples.