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On a characterization of finite Blaschke products

Complex Variables and Elliptic Equations, 2014
International audienceWe study the convergence of a sequence of finite Blaschke products of a fix order toward a rotation.
Javad Mashreghi
exaly   +4 more sources

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Hyperbolic Distortion, Boundary Behaviour and Finite Blaschke Products

Computational Methods and Function Theory, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nina Zorboska, Zorboska Nina
exaly   +2 more sources

Commuting finite Blaschke products with no fixed points in the unit disk

Journal of Mathematical Analysis and Applications, 2009
In this paper we study when two finite Blaschke products commute. We complete previous results by Chalendar and Mortini (when they have a fixed point in the unit disk) and by Arteaga (when they do not have a fixed point in the unit disk)
Manuela Basallote, Manuel D Contreras
exaly   +3 more sources

A decomposition of finite blaschke products

Complex Variables, Theory and Application: An International Journal, 1995
The primary purpose of this work was to study decompositions of finite Blaschke products. We found that if a finite Blaschke product B could be written as B∘h = B where h is a nontrivial holomorphic function from the unit disk into the unit disk, then B could be decomposed into a composition of two finite Blaschke products of lower order.
R. L. Craighead, F. W. Carroll
openaire   +1 more source

Finite Products of Interpolating Blaschke Products

Journal of the London Mathematical Society, 1994
The main result of this paper is a characterization of the Blaschke products \(B\) which are such that \(\tau_ \alpha (B)\) is a finite product of interpolating Blaschke products for all \(\alpha \in D\), the unit disc. That is Theorem. Let \(B\) be a finite product of interpolating Blaschke products. Let \(\{z_ n\}\) be the sequence of zeros of \(B\),
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Commuting finite Blaschke products

Ergodic Theory and Dynamical Systems, 1999
We consider the set of finite Blaschke products $F$ for which the fixed points on the circle $S^1$ are expanding and we prove that if $F'(x) \ne F'(y)$ for all different fixed points $x,y$ of $F$ on $S^1$, then $F$ commutes only with its own powers.
openaire   +1 more source

Approximation by Finite Blaschke Products

2018
Although finite Blaschke products are a remarkable and exclusive class of functions, they appear in many important approximation problems.
Stephan Ramon Garcia, Javad Mashreghi, William T. Ross   +2 more
openaire   +1 more source

Expanding a Finite Blaschke Product

Complex Variables, Theory and Application: An International Journal, 2002
It is shown that a finite Blaschke product with finite poles, has a nonzero residue. The proofs for the two types of Blaschke products are essentially different.
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Finite Blaschke Products: The Basics

2018
For a finite sequence z1, z2, …, zn in \(\mathbb {D}\) and \(\gamma \in \mathbb {T}\), the function $$\displaystyle B(z) = \gamma \prod _{k=1}^{n} \frac {z - z_k}{1-\overline {z_k} z} $$ is a finite Blaschke product.
Stephan Ramon Garcia, Javad Mashreghi, William T. Ross   +2 more
openaire   +1 more source

Boundary Interpolation by Finite Blaschke Products

Constructive Approximation, 2006
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.
Pamela Gorkin, Robert C. Rhoades
openaire   +1 more source