Convergent Interpolation to Cauchy Integrals over Analytic Arcs.
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| Title: | Convergent Interpolation to Cauchy Integrals over Analytic Arcs. |
|---|---|
| Authors: | Baratchart, Laurent1 laurent.baratchart@sophia.inria.fr, Yattselev, Maxim1 myattsel@sophia.inria.fr |
| Source: | Foundations of Computational Mathematics. Dec2009, Vol. 9 Issue 6, p675-715. 41p. 2 Graphs. |
| Subjects: | Cauchy transform, Complex numbers, Interpolation, Differential equations, Asymptotic theory of algebraic ideals, Equilibrium |
| Abstract: | We consider multipoint Padé approximation to Cauchy transforms of complex measures. We show that if the support of a measure is an analytic Jordan arc and if the measure itself is absolutely continuous with respect to the equilibrium distribution of that arc with Dini-smooth nonvanishing density, then the diagonal multipoint Padé approximants associated with appropriate interpolation schemes converge locally uniformly to the approximated Cauchy transform in the complement of the arc. This asymptotic behavior of Padé approximants is deduced from the analysis of underlying non-Hermitian orthogonal polynomials, for which we use classical properties of Hankel and Toeplitz operators on smooth curves. A construction of the appropriate interpolation schemes is explicit granted the parametrization of the arc. [ABSTRACT FROM AUTHOR] |
| Copyright of Foundations of Computational Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Convergent Interpolation to Cauchy Integrals over Analytic Arcs. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Baratchart%2C+Laurent%22">Baratchart, Laurent</searchLink><relatesTo>1</relatesTo><i> laurent.baratchart@sophia.inria.fr</i><br /><searchLink fieldCode="AR" term="%22Yattselev%2C+Maxim%22">Yattselev, Maxim</searchLink><relatesTo>1</relatesTo><i> myattsel@sophia.inria.fr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Foundations+of+Computational+Mathematics%22">Foundations of Computational Mathematics</searchLink>. Dec2009, Vol. 9 Issue 6, p675-715. 41p. 2 Graphs. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Cauchy+transform%22">Cauchy transform</searchLink><br /><searchLink fieldCode="DE" term="%22Complex+numbers%22">Complex numbers</searchLink><br /><searchLink fieldCode="DE" term="%22Interpolation%22">Interpolation</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+theory+of+algebraic+ideals%22">Asymptotic theory of algebraic ideals</searchLink><br /><searchLink fieldCode="DE" term="%22Equilibrium%22">Equilibrium</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We consider multipoint Padé approximation to Cauchy transforms of complex measures. We show that if the support of a measure is an analytic Jordan arc and if the measure itself is absolutely continuous with respect to the equilibrium distribution of that arc with Dini-smooth nonvanishing density, then the diagonal multipoint Padé approximants associated with appropriate interpolation schemes converge locally uniformly to the approximated Cauchy transform in the complement of the arc. This asymptotic behavior of Padé approximants is deduced from the analysis of underlying non-Hermitian orthogonal polynomials, for which we use classical properties of Hankel and Toeplitz operators on smooth curves. A construction of the appropriate interpolation schemes is explicit granted the parametrization of the arc. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Foundations of Computational Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10208-009-9042-8 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 41 StartPage: 675 Subjects: – SubjectFull: Cauchy transform Type: general – SubjectFull: Complex numbers Type: general – SubjectFull: Interpolation Type: general – SubjectFull: Differential equations Type: general – SubjectFull: Asymptotic theory of algebraic ideals Type: general – SubjectFull: Equilibrium Type: general Titles: – TitleFull: Convergent Interpolation to Cauchy Integrals over Analytic Arcs. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Baratchart, Laurent – PersonEntity: Name: NameFull: Yattselev, Maxim IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2009 Type: published Y: 2009 Identifiers: – Type: issn-print Value: 16153375 Numbering: – Type: volume Value: 9 – Type: issue Value: 6 Titles: – TitleFull: Foundations of Computational Mathematics Type: main |
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