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Mat. Zametki, 2010, Volume 87, Issue 4, Pages 604–615 (Mi mz7708)  

This article is cited in 2 scientific papers (total in 2 papers)

On the Phenomenon of Spurious Interpolation of Elliptic Functions by Diagonal Padé Approximants

D. V. Khristoforov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We study diagonal Padé approximants for elliptic functions. The presence of spurious poles in the approximants not corresponding to the singularities of the original function prevents uniform convergence of the approximants in the Stahl domain. This phenomenon turns out to be closely related to the existence in the Stahl domain of points of spurious interpolation at which the Padé approximants interpolate the other branch of the elliptic function. We also investigate the behavior of diagonal Padé approximants in a neighborhood of points of spurious interpolation.

Keywords: elliptic function, diagonal Padé approximants, spurious pole, spurious interpolation, Stahl compact set, Laurent series, Riemann surface, complex Green function

DOI: https://doi.org/10.4213/mzm7708

Full text: PDF file (517 kB)
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English version:
Mathematical Notes, 2010, 87:4, 564–574

Bibliographic databases:

UDC: 517.53
Received: 31.03.2009
Revised: 29.10.2009

Citation: D. V. Khristoforov, “On the Phenomenon of Spurious Interpolation of Elliptic Functions by Diagonal Padé Approximants”, Mat. Zametki, 87:4 (2010), 604–615; Math. Notes, 87:4 (2010), 564–574

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. S. Lubinsky, “Exact interpolation, spurious poles, and uniform convergence of multipoint Padé approximants”, Sb. Math., 209:3 (2018), 432–448  mathnet  crossref  crossref  adsnasa  isi  elib
    2. Lubinsky D.S., “On Uniform Convergence of Diagonal Multipoint Pade Approximants For Entire Functions”, Constr. Approx., 49:1 (2019), 149–174  crossref  mathscinet  zmath  isi  scopus
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