## Spacing properties of the zeros of orthogonal polynomials on Cantor sets via a sequence of polynomial mappings

 dc.citation.epage 522 en_US dc.citation.issueNumber 2 en_US dc.citation.spage 509 en_US dc.citation.volumeNumber 149 en_US dc.contributor.author Alpan, G. en_US dc.date.accessioned 2018-04-12T10:57:31Z dc.date.available 2018-04-12T10:57:31Z dc.date.issued 2016 en_US dc.department Department of Mathematics en_US dc.description.abstract Let μ be a probability measure with an infinite compact support on R. Let us further assume that Fn: = fn∘ ⋯ ∘ f1 is a sequence of orthogonal polynomials for μ where (fn)n=1 ∞ is a sequence of nonlinear polynomials. We prove that if there is an s0∈ N such that 0 is a root of fn′ for each n> s0 then the distance between any two zeros of an orthogonal polynomial for μ of a given degree greater than 1 has a lower bound in terms of the distance between the set of critical points and the set of zeros of some Fk. Using this, we find sharp bounds from below and above for the infimum of distances between the consecutive zeros of orthogonal polynomials for singular continuous measures. © 2016, Akadémiai Kiadó, Budapest, Hungary. en_US dc.identifier.doi 10.1007/s10474-016-0628-8 en_US dc.identifier.issn 2365294 dc.identifier.uri http://hdl.handle.net/11693/36925 dc.language.iso English en_US dc.publisher Springer Netherlands en_US dc.relation.isversionof http://dx.doi.org/10.1007/s10474-016-0628-8 en_US dc.source.title Acta Mathematica Hungarica en_US dc.subject orthogonal polynomial en_US dc.subject singular continuous measure en_US dc.subject zero spacing en_US dc.title Spacing properties of the zeros of orthogonal polynomials on Cantor sets via a sequence of polynomial mappings en_US dc.type Article en_US
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