File Download
  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Higher-Order, Polar and Sz.-Nagy’s Generalized Derivatives of Random Polynomials with Independent and Identically Distributed Zeros on the Unit Circle

TitleHigher-Order, Polar and Sz.-Nagy’s Generalized Derivatives of Random Polynomials with Independent and Identically Distributed Zeros on the Unit Circle
Authors
KeywordsRandom polynomial
Zero distribution
Polar derivative
Sz.-Nagy’s generalized derivative
Issue Date2015
Citation
Computational Methods and Function Theory, 2015, v. 15 n. 1, p. 159-186 How to Cite?
AbstractFor random polynomials with independent and identically distributed (i.i.d.) zeros following any common probability distribution μ with support contained in the unit circle, the empirical measures of the zeros of their first and higher-order derivatives will be proved to converge weakly to μ almost surely (a.s.). This, in particular, completes a recent work of Subramanian on the first-order derivative case where μ was assumed to be non-uniform. The same almost sure weak convergence will also be shown for polar and Sz.-Nagy’s generalized derivatives, assuming some mild conditions.
Persistent Identifierhttp://hdl.handle.net/10722/210741
ISSN
2023 Impact Factor: 0.6
2023 SCImago Journal Rankings: 0.448
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorCheung, PL-
dc.contributor.authorNg, TW-
dc.contributor.authorTsai, HTJ-
dc.contributor.authorYam, SCP-
dc.date.accessioned2015-06-23T05:49:02Z-
dc.date.available2015-06-23T05:49:02Z-
dc.date.issued2015-
dc.identifier.citationComputational Methods and Function Theory, 2015, v. 15 n. 1, p. 159-186-
dc.identifier.issn1617-9447-
dc.identifier.urihttp://hdl.handle.net/10722/210741-
dc.description.abstractFor random polynomials with independent and identically distributed (i.i.d.) zeros following any common probability distribution μ with support contained in the unit circle, the empirical measures of the zeros of their first and higher-order derivatives will be proved to converge weakly to μ almost surely (a.s.). This, in particular, completes a recent work of Subramanian on the first-order derivative case where μ was assumed to be non-uniform. The same almost sure weak convergence will also be shown for polar and Sz.-Nagy’s generalized derivatives, assuming some mild conditions.-
dc.languageeng-
dc.relation.ispartofComputational Methods and Function Theory-
dc.rightsThis is a post-peer-review, pre-copyedit version of an article published in Computational Methods and Function Theory. The final authenticated version is available online at: https://doi.org/10.1007/s40315-014-0097-4-
dc.subjectRandom polynomial-
dc.subjectZero distribution-
dc.subjectPolar derivative-
dc.subjectSz.-Nagy’s generalized derivative-
dc.titleHigher-Order, Polar and Sz.-Nagy’s Generalized Derivatives of Random Polynomials with Independent and Identically Distributed Zeros on the Unit Circle-
dc.typeArticle-
dc.identifier.emailNg, TW: ngtw@hku.hk-
dc.identifier.authorityNg, TW=rp00768-
dc.description.naturepostprint-
dc.identifier.doi10.1007/s40315-014-0097-4-
dc.identifier.scopuseid_2-s2.0-84924331216-
dc.identifier.hkuros243939-
dc.identifier.volume15-
dc.identifier.issue1-
dc.identifier.spage159-
dc.identifier.epage186-
dc.identifier.eissn2195-3724-
dc.identifier.isiWOS:000350674900011-
dc.identifier.issnl1617-9447-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats