scholarly journals Finite Blaschke products with prescribed critical points, Stieltjes polynomials, and moment problems

2017 ◽  
Vol 9 (1) ◽  
pp. 221-249 ◽  
Author(s):  
Gunter Semmler ◽  
Elias Wegert
Keyword(s):  
Critical Points ◽  
Moment Problems ◽  
Blaschke Products ◽  
Finite Blaschke Products

Finite Blaschke Products: The Basics

2018 ◽  
pp. 39-58
Author(s):  
Stephan Ramon Garcia ◽  
Javad Mashreghi ◽  
William T. Ross
Keyword(s):  
Blaschke Products ◽  
Finite Blaschke Products

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

2009 ◽  
Vol 359 (2) ◽  
pp. 547-555 ◽  
Author(s):  
Manuela Basallote ◽  
Manuel D. Contreras ◽  
Carmen Hernández-Mancera
Keyword(s):  
Fixed Points ◽  
Unit Disk ◽  
Blaschke Products ◽  
Finite Blaschke Products

scholarly journals On the differentiability ofT(r,f)

1982 ◽  
Vol 5 (2) ◽  
pp. 351-356
Author(s):  
Douglas W. Townsed
Keyword(s):  
Blaschke Products ◽  
Finite Blaschke Products

It is well known thatT(r,f)is differentiable at least forr>r0. We show that, in fact,T(r,f)is differentiable for all but at most one value ofr, and ifT(r,f)fails to have a derivative for some value ofr, thenfis a constant times a quotient of finite Blaschke products.

Commuting finite Blaschke products

1999 ◽  
Vol 19 (3) ◽  
pp. 549-552 ◽  
Author(s):  
CARLOS ARTEAGA
Keyword(s):  
Fixed Points ◽  
Blaschke Products ◽  
Finite Blaschke Products

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.

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