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Article: Ritt's theory on the unit disk

TitleRitt's theory on the unit disk
Authors
KeywordsRitt's theory
Finite maps
Fundamental groups
Monodromy
Finite Blaschke products
Issue Date2013
PublisherWalter de Gruyter GmbH & Co KG.
Citation
Forum Mathematicum, 2013, v. 25 n. 4, p. 821-851 How to Cite?
AbstractThe 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 Identifierhttp://hdl.handle.net/10722/135166
ISSN
2015 Impact Factor: 0.823
2015 SCImago Journal Rankings: 0.848
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorNg, TWen_US
dc.contributor.authorWang, MX-
dc.date.accessioned2011-07-27T01:29:13Z-
dc.date.available2011-07-27T01:29:13Z-
dc.date.issued2013en_US
dc.identifier.citationForum Mathematicum, 2013, v. 25 n. 4, p. 821-851en_US
dc.identifier.issn0933-7741-
dc.identifier.urihttp://hdl.handle.net/10722/135166-
dc.description.abstractThe 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.languageengen_US
dc.publisherWalter de Gruyter GmbH & Co KG.-
dc.relation.ispartofForum Mathematicumen_US
dc.rightsThe final publication is available at www.degruyter.com-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectRitt's theory-
dc.subjectFinite maps-
dc.subjectFundamental groups-
dc.subjectMonodromy-
dc.subjectFinite Blaschke products-
dc.titleRitt's theory on the unit disken_US
dc.typeArticleen_US
dc.identifier.emailNg, TW: ngtw@hku.hken_US
dc.identifier.emailWang, MX: shankly@hkusua.hku.hken_US
dc.identifier.authorityNg, TW=rp00768en_US
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1515/form.2011.136-
dc.identifier.scopuseid_2-s2.0-84884661374-
dc.identifier.hkuros188288en_US
dc.identifier.volume25-
dc.identifier.issue4-
dc.identifier.spage821-
dc.identifier.epage851-
dc.identifier.eissn1435-5337-
dc.identifier.isiWOS:000321253600006-
dc.publisher.placeGermany-

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