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Ritt's theory on the unit disk
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Veröffentlicht/Copyright:
1. Juli 2013
Abstract.
The aim of this paper is to revisit Ritt's theory from a topological perspective by extensively using the concept of fundamental groups. This enables us to regard the theory as an example which illustrates many ideas of a letter of Grothendieck and to put Ritt's theory into a more general analytic setting. In particular, Ritt's theory on the unit disk will be carefully developed and a special class of finite Blaschke products will be introduced as the counterpart of Chebyshev polynomials in Ritt's theory. These finite Blaschke products will be shown to be closely related to the elliptic rational functions, which are of great importance in the filter design theory.
Keywords: Ritt's theory; finite maps; fundamental groups; monodromy; finite
Blaschke products; Jacobian elliptic functions
Received: 2010-12-23
Revised: 2011-04-26
Published Online: 2013-07-01
Published in Print: 2013-07-01
© 2013 by Walter de Gruyter Berlin Boston
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- 𝔬K0-quasi-abelian varieties with complex multiplication
- Basic properties of nonsmooth Hörmander's vector fields and Poincaré's inequality
- Continuity property for the commutators of multilinear Calderón–Zygmund operators
- Characterizations of Besov and Triebel–Lizorkin spaces on metric measure spaces
- Ritt's theory on the unit disk
- A short note on the existence of nontrivial solutions to the vectorial equation in H01(Ω)N
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Schlagwörter für diesen Artikel
Ritt's theory;
finite maps;
fundamental groups;
monodromy;
finite
Blaschke products;
Jacobian elliptic functions
Artikel in diesem Heft
- Masthead
- A note on the L-theory of infinite product categories
- 𝔬K0-quasi-abelian varieties with complex multiplication
- Basic properties of nonsmooth Hörmander's vector fields and Poincaré's inequality
- Continuity property for the commutators of multilinear Calderón–Zygmund operators
- Characterizations of Besov and Triebel–Lizorkin spaces on metric measure spaces
- Ritt's theory on the unit disk
- A short note on the existence of nontrivial solutions to the vectorial equation in H01(Ω)N
- Characterization of finitely generated infinitely iterated wreath products
