# Questions tagged [blaschke-products]

Use this tag for questions related to Blaschke products, which are bounded analytic functions in the open unit disk constructed to have zeros at a (finite or infinite) sequence of prescribed complex numbers inside the unit disk.

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### Characterizing the unimodular functions from the closed disk $\mathbb{C}$ to $\mathbb{C}$ with constraints

It is well known that if $f:\mathbb{D}\to\mathbb{C}$ is analytic, continuous on the boundary, and is unimodular (say with a finite number of zeros) then $f$ is a finite Blaschke product up to some ...
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### Real-valued bounded analytic functions on the unit disc

Let $f: \overline{\mathbb{D}} \to \mathbb{R}^+$ be a real (positive) valued function on the closed unit disc that is bounded and analytic on $\mathbb{D}$ (open unit disc) and \lim_{|z| \to 1}f(z) = ...
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### Hankel operator with symbol a Blaschke product

If $B={\prod}_j \varphi_j$ is a Blaschke product (finite or infinite) of Blaschke factors $\varphi_j(w)=\frac{w-\alpha_j}{1-\overline{\alpha_j}w}$ with $|\alpha_j|>1$, is it true that the norm of ...
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### Each point on the unit circle accumulation point of interpolating sequence?

I have an interpolating sequence for $H^\infty(\mathbb D)$ in the unit disk (that is, a uniformly separated sequence) which, in addition, satisfies the Blaschke condition. Is it possible that each ...
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### How can we draw a Blaschke $3$ ellipse?

Today I read the article Ellipses and Finite Blaschke Products by Ulrich Daepp, Pamela Gorkin, and Raymond Mortini. In there they have proved very nice geometric results about per-images of Blaschke ...
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I would like to make my previous question more precise. If $B$ is a finite Blaschke product such that its Julia set $J_B$ is a Cantor subset of $S^1$, then is it true that $B$ is expanding on $J_B\,$?...