Skip Navigation

International Mathematics Research Papers (2008) Vol. 2008 : article ID rpm007, 128 pages, doi:10.1093/imrp/rpm007 published on January 29, 2008
This Article
Right arrow Full Text (PDF)
Right arrow References
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Aptekarev, A. I.
Right arrow Articles by Van Assche, W.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Asymptotics of Hermite–Padé Rational Approximants for Two Analytic Functions with Separated Pairs of Branch Points (Case of Genus 0)

Alexander I. Aptekarev1, Arno B. J. Kuijlaars2 and Walter Van Assche2

1 Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Square 4, 125047 Moscow, Russian Federation
2 Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B box 2400, BE-3001 Leuven, Belgium

Correspondence: Correspondence to be sent to: Walter Van Assche, Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B box 2400, BE-3001 Leuven, Belgium. e-mail: walter{at}wis.kuleuven.be

We investigate the asymptotic behavior for type II Hermite–Padé approximation to two functions, where each function has two branch points and the pairs of branch points are separated. We give a classification of the cases such that the limiting counting measures for the poles of the Hermite–Padé approximants are described by an algebraic function h of order and genus 0. This situation gives rise to a vector-potential equilibrium problem for measures {lambda}, µ1, and µ2, and the poles of the common denominator are asymptotically distributed like {lambda}/2. We also work out the strong asymptotics for the corresponding Hermite–Padé approximants by using a 3 x 3 Riemann–Hilbert problem that characterizes this Hermite–Padé approximation problem.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.