RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

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

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)
References: PDF file   HTML file

English version:
Mathematical Notes, 2010, 87:4, 564–574

Bibliographic databases:

UDC: 517.53
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
\Bibitem{Khr10} \by D.~V.~Khristoforov \paper On the Phenomenon of Spurious Interpolation of Elliptic Functions by Diagonal Pad\'e Approximants \jour Mat. Zametki \yr 2010 \vol 87 \issue 4 \pages 604--615 \mathnet{http://mi.mathnet.ru/mz7708} \crossref{https://doi.org/10.4213/mzm7708} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2762747} \zmath{https://zbmath.org/?q=an:05791085} \elib{http://elibrary.ru/item.asp?id=15321866} \transl \jour Math. Notes \yr 2010 \vol 87 \issue 4 \pages 564--574 \crossref{https://doi.org/10.1134/S000143461003034X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000279034600034} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77954016141} 

• http://mi.mathnet.ru/eng/mz7708
• https://doi.org/10.4213/mzm7708
• http://mi.mathnet.ru/eng/mz/v87/i4/p604

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. Lubinsky D.S., “On Uniform Convergence of Diagonal Multipoint Pade Approximants For Entire Functions”, Constr. Approx., 49:1 (2019), 149–174
•  Number of views: This page: 252 Full text: 52 References: 22 First page: 7