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Commuting finite Blaschke products
Ergodic Theory and Dynamical Systems, 1999We 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.
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VALUE DISTRIBUTION OF INTERPOLATING BLASCHKE PRODUCTS
Journal of the London Mathematical Society, 2005Given an inner function \(u\) and a complex number \(a\in\mathbb D\), the function \(u_a:=(a-u)(1-\overline a u)^{-1}\) is called the Frostamn shift of \(u\). The celebrated Frostman's theorem claims that \(u_a\) is a Blaschke product unless \(a\) belongs to some exceptional set \(E(u)\) of logarithmic capacity zero. McLaughlin and Piranian showed that
Gorkin, Pamela, Mortini, Raymond
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ON BOUNDARY BEHAVIOUR OF BLASCHKE PRODUCTS
Analysis, 1986If \(B(z,z_ n)\) is a Blaschke product in the unit disk whose zeros \(z_ n\) have limit point \(e^{i\theta}\), then B and its subproducts have an angular limit of modulus 1 at \(e^{i\theta}\) iff the Frostman condition \(\sum (1-| z_ n|)/| e^{i\theta}-z|
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Minimal Interpolation by Blaschke Products II
Bulletin of the London Mathematical Society, 1988[For part I see the author in J. Lond. Math. Soc., II. Ser. 32, 488-496 (1985; Zbl 0595.30048).] Let U denote the class of holomorphic functions in the unit disk \(D=\{| z|
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Absolutely continuous conjugacies of Blaschke products III
Journal d'Analyse Mathématique, 1994Let \(f\) be a Blaschke product in the unit disk \(\mathbb{D}\). Its Julia set is the entire unit circle \(S\) if and only if it is ergodic. Let \(\varphi\) denote an absolutely continuous homeomorphism of \(S\) onto itself. In an earlier paper the author showed that \(\varphi \circ f \circ \varphi^{- 1}\) can be a Blaschke product only in the trivial ...
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IDEALS GENERATED BY INTERPOLATING BLASCHKE PRODUCTS
Analysis, 1994Let \(M(H^ \infty)\) denote the maximal ideal space of \(H^ \infty(D)\), where \(H^ \infty\) is the Banach algebra of bounded analytic functions in the open unit disk \(D= \{z\in \mathbb{C}: | z|< 1\}\). Let \(f\in H^ \infty\) and let \(Z(f)= \{m\in M(H^ \infty): f(m)= 0\}\).
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Blaschke--Santaló Diagram for Volume, Perimeter, and First Dirichlet Eigenvalue
SIAM Journal on Mathematical Analysis, 2021Ilias Ftouhi
exaly
2017
In a recent joint work with Mingxi Wang, a version of Ritt's theory on the factorization of finite Blaschke products has been developed. In this Ritt's theory on the unit disk, a special class of finite Blaschke products has been introduced as the counterpart of Chebyshev polynomials in Ritt's theory for polynomials.
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In a recent joint work with Mingxi Wang, a version of Ritt's theory on the factorization of finite Blaschke products has been developed. In this Ritt's theory on the unit disk, a special class of finite Blaschke products has been introduced as the counterpart of Chebyshev polynomials in Ritt's theory for polynomials.
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