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Article: Ritt's theory on the unit disk
Title | Ritt's theory on the unit disk |
---|---|
Authors | |
Keywords | Ritt's theory Finite maps Fundamental groups Monodromy Finite Blaschke products Jacobian elliptic functions |
Issue Date | 2013 |
Publisher | Walter de Gruyter GmbH & Co KG. |
Citation | Forum Mathematicum, 2013, v. 25 n. 4, p. 821-851 How to Cite? |
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. |
Persistent Identifier | http://hdl.handle.net/10722/135166 |
ISSN | 2023 Impact Factor: 1.0 2023 SCImago Journal Rankings: 0.692 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Ng, TW | en_US |
dc.contributor.author | Wang, MX | - |
dc.date.accessioned | 2011-07-27T01:29:13Z | - |
dc.date.available | 2011-07-27T01:29:13Z | - |
dc.date.issued | 2013 | en_US |
dc.identifier.citation | Forum Mathematicum, 2013, v. 25 n. 4, p. 821-851 | en_US |
dc.identifier.issn | 0933-7741 | - |
dc.identifier.uri | http://hdl.handle.net/10722/135166 | - |
dc.description.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. | - |
dc.language | eng | en_US |
dc.publisher | Walter de Gruyter GmbH & Co KG. | - |
dc.relation.ispartof | Forum Mathematicum | en_US |
dc.rights | © de Gruyter 2013. The final publication is available at www.degruyter.com | - |
dc.subject | Ritt's theory | - |
dc.subject | Finite maps | - |
dc.subject | Fundamental groups | - |
dc.subject | Monodromy | - |
dc.subject | Finite Blaschke products | - |
dc.subject | Jacobian elliptic functions | - |
dc.title | Ritt's theory on the unit disk | en_US |
dc.type | Article | en_US |
dc.identifier.email | Ng, TW: ngtw@hku.hk | en_US |
dc.identifier.email | Wang, MX: shankly@hkusua.hku.hk | en_US |
dc.identifier.authority | Ng, TW=rp00768 | en_US |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1515/form.2011.136 | - |
dc.identifier.scopus | eid_2-s2.0-84884661374 | - |
dc.identifier.hkuros | 188288 | en_US |
dc.identifier.volume | 25 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 821 | - |
dc.identifier.epage | 851 | - |
dc.identifier.eissn | 1435-5337 | - |
dc.identifier.isi | WOS:000321253600006 | - |
dc.publisher.place | Germany | - |
dc.identifier.issnl | 0933-7741 | - |