Unicritical Blaschke Products and Domains of Ellipticity

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

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...

Boundary Interpolation by Finite Blaschke Products

Given 2n distinct points z1, z′ 1, z2, z ′ 2, . . . , zn, z ′ n (in this order) on the unit circle, and n points w1, . . . , wn on the unit circle, we show how to construct a Blaschke product B of degree n such that B(zj) = wj for all j and, in addition, B(z′ j) = B(z ′ k) for all j and k. Modifying this example yields a Blaschke product of degree n− 1 that interpolates the zj ’s to the wj ’s. ...

Contractivity of the H∞-calculus and Blaschke products

It is well known that a densely defined operator A on a Hilbert space is accretive if and only if A has a contractive H∞-calculus for any angle bigger than π 2 . A third equivalent condition is that ‖(A− w)(A + w)−1‖ ≤ 1 for all Rew ≥ 0. In the Banach space setting, accretivity does not imply the boundedness of the H∞-calculus any more. However, we show in this note that the last condition is s...