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Matematicheskie Zametki, 2010, Volume 87, Issue 4, Pages 604–615
DOI: https://doi.org/10.4213/mzm7708 (Mi mzm7708) 		 
This article is cited in 3 scientific papers (total in 3 papers)

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

D. V. Khristoforov

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (517 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm7708
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.
Received: 31.03.2009
Revised: 29.10.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 4, Pages 564–574
DOI: https://doi.org/10.1134/S000143461003034X
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
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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  • https://doi.org/10.4213/mzm7708
  • https://www.mathnet.ru/eng/mzm/v87/i4/p604
    • This publication is cited in the following 3 articles:
    1. 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
    2. Doron S. Lubinsky, Applied and Numerical Harmonic Analysis, Topics in Classical and Modern Analysis, 2019, 241  crossref
    3. D. S. Lubinsky, “Exact interpolation, spurious poles, and uniform convergence of multipoint Padé approximants”, Sb. Math., 209:3 (2018), 432–448  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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