Zero sets of interpolating Blaschke products

AN Lp DEFINITION OF INTERPOLATING BLASCHKE PRODUCTS

Interpolating Blaschke Products and Angular Derivatives

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra H∞[b : b has finite angular derivative everywhere]. We study the most well-known example of a Blaschke product with infinite angular deriva...

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...

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.