Norms of Composition Operators Induced by Finite Blaschke Products on Möbius Invariant Spaces

2013 ◽  
pp. 209-222
Author(s):  
María J. Martín ◽  
Dragan Vukotić
Keyword(s):  
Composition Operators ◽  
Blaschke Products ◽  
Finite Blaschke Products ◽  
Invariant Spaces

scholarly journals When do finite Blaschke products commute?

2001 ◽  
Vol 64 (2) ◽  
pp. 189-200 ◽  
Author(s):  
Isabelle Chalendar ◽  
Raymond Mortini
Keyword(s):  
Composition Operators ◽  
Blaschke Products ◽  
Finite Blaschke Products

We study the following questions. Which finite Blaschke products are eigenvectors of the composition operatorsTu:f↦f∘u, what are the possible eigenvalues, and which pairs (B,C) of finite Blaschke products commute (that is, satisfyB∘C=C∘B).

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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