Results 141 to 150 of about 267 (174)

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.
Robert C Rhoades, Gorkin Pamela
exaly   +2 more sources

Family of Finite Blaschke Products in $$C^*$$-Algebras

Mathematical Notes
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A Yu Kuznetsova, Kuznetsova A Yu
exaly   +3 more sources

Finite Blaschke product interpolation on the closed unit disc

Journal of Mathematical Analysis and Applications, 2002
We show how to construct all finite Blaschke product solutions and the minimal scaled Blaschke product solution to the Nevanlinna–Pick interpolation problem in the open unit disc by solving eigenvalue problems of the interpolation data. Based on a result
Christer Glader, Mikael Lindstrom
exaly   +2 more sources

Critical Values of Finite Blaschke Products

Doklady Mathematics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 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 \(B\),
openaire   +2 more sources

Polynomials Versus Finite Blaschke Products

2013
The aim of this chapter is to compare polynomials of one complex variable and finite Blaschke products and demonstrate that they share many similar properties. In fact, we collect many known results as well as some very recent results for finite Blaschke products here to establish a dictionary between polynomials and finite Blaschke products.
Tsang, CY, Ng, PTW
openaire   +2 more sources

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

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