Level-sets of special Blaschke products.

Exceptional sets for the derivatives of Blaschke products

is the Nevanlinna characteristic of f [13]. Meromorphic functions of finite order have been extensively studied and they have numerous applications in pure and applied mathematics, e.g. in linear differential equations. In many applications a major role is played by the logarithmic derivative of meromorphic functions and we need to obtain sharp estimates for the logarithmic derivative as we app...

Blaschke Sets for Bergman Spaces

where dist denotes the Euclidean distance. Note that for Lipα(D) and A∞ the zero sequences Z are characterized by (1) and (2), with S replaced by Z. 3. The Blaschke sets S for the class D of analytic functions with finite Dirichlet integral are characterized by (2) (see [B]). Note that D-zero sequences cannot be described this way because there are f ∈ D whose zeros come arbitrarily close to ev...

Products of Special Sets of Real Numbers

We develop a machinery which translates results on algebraic sums of sets of reals into the corresponding results on their cartesian product. Some consequences are: (1) The product of meager/null-additive sets in the Cantor space is meager/nulladditive, respectively. (2) The product of a meager/null-additive set and a strong measure zero/strongly meager set in the Cantor space has strong measur...

Computable Analysis and Blaschke Products

We show that if a Blaschke product defines a computable function, then it has a computable sequence of zeros in which the number of times each zero is repeated is its multiplicity. We then show that the converse is not true. We finally show that every computable, radial, interpolating sequence yields a computable Blaschke product.

AN Lp DEFINITION OF INTERPOLATING BLASCHKE PRODUCTS