# 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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### 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 ...
If $a_n\in\mathbb{C}$ are complex number such that $|a_n|<1$ and $\sum_{n}(1-|a_n|)<\infty$, then I know that following Blaschke product define an analytic function on the open unit disk $\... 1 vote 0 answers 280 views ### Zeros of bounded analytic function on unit disk -- infinite Blaschke product [duplicate] Suppose we have$f: \mathbb{D} \rightarrow \mathbb{D}$analytic and not identically zero. In order to prove$f$has an infinite Blaschke product representation (where of course the product defines an ... 0 votes 1 answer 118 views ### Univalent Blaschke Products on$\mathbb{D}$Let$B$be a finite Blaschke product of degree$n$. Suppose there exist an open subset$U$of$\mathbb{D}$such that$B$is univalent on$U.$Is it true that$n=1$? 5 votes 1 answer 3k views ### Analytic function on unit disk has finitely many zeros I am studying complex analysis from Theodore Gamelin's text and Exercise 1 of chapter IX.2 says that if$f$is analytic inside the open unit disk and continuous on its boundary that satisfies$|f(z)| =...
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 $J_B\,$?...