Widow factors for the Hilbert norm

dc.citation.epage18en_US
dc.citation.spage11en_US
dc.citation.volumeNumber107en_US
dc.contributor.authorAlpan, G.en_US
dc.contributor.authorGoncharov, A.en_US
dc.date.accessioned2019-01-30T07:09:42Z
dc.date.available2019-01-30T07:09:42Z
dc.date.issued2015en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractGiven a probability measure µ with non-polar compact support K, we define the n-th Widom factor W2n(µ) as the ratio of the Hilbert norm of the monic n-th orthogonal polynomial and the n-th power of the logarithmic capacity of K. If µ is regular in the Stahl–Totik sense then the sequence (W2n(µ))∞n=0 has subexponential growth. For measures from the Szegő class on [−1, 1] this sequence converges to some proper value. We calculate the corresponding limit for the measure that generates the Jacobi polynomials, analyze the behavior of the corresponding limit as a function of the parameters and review some other examples of measures when Widom factors can be evaluated.en_US
dc.identifier.doi10.4064/bc107-0-1en_US
dc.identifier.eissn1732-8985
dc.identifier.issn0239-7269
dc.identifier.urihttp://hdl.handle.net/11693/48500
dc.language.isoEnglishen_US
dc.publisherPolska Akademia Nauken_US
dc.relation.isversionofhttps://doi.org/10.4064/bc107-0-1en_US
dc.source.titleInstitute of Mathematıcs Polish Academy of Sciencesen_US
dc.titleWidow factors for the Hilbert normen_US
dc.typeArticleen_US
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