Please use this identifier to cite or link to this item: http://hdl.handle.net/10016/6367

 Google™ Scholar. Others By: Barrios, Dolores - López Lagomasino, Guillermo - Martínez-Finkelshtein, Andrei - Torrano, Emilio
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 Title: On the domain of convergence and poles of complex J-fractions Author(s): Barrios, DoloresLópez Lagomasino, GuillermoMartínez-Finkelshtein, AndreiTorrano, Emilio Publisher: Elsevier Issued date: May-1998 Citation: Journal of Approximation Theory, 1998, vol. 93, n. 2, p. 177-200 URI: http://hdl.handle.net/10016/6367 ISSN: 0021-9045 DOI: 10.1006/jath.1998.3165 Description: 24 pages, no figures.-- MSC2000 code: 30B60.MR#: MR1616769 (99b:30003)Zbl#: Zbl 0909.30002 Abstract: Consider the infinite $J$-fraction $$\cfrac a_0 \\ z-b_0-\cfrac a_1 \\ z-b_1-\cfrac a_2 \\ z-b_2-{\lower6pt\hbox{\ddots}}\endcfrac$$ where $a_n\in{\bf C}\sbs\{0\},\ b_n\in{\bf C}$. Under very general conditions on the coefficients $\{a_n\},\ \{b_n\}$, we prove that this continued fraction coverges to a meromorphic function in ${\bf C}\sbs{\bf R}$. Such conditions hold, in particular, if $\lim_n{\rm Im}(a_n)=\lim_n{\rm Im}(b_n)=0$ and $\sum_{n\ge0}(1/ _n =\infty$ (or $\sum_{n\ge0}( _n _na_{n+1} =\infty)$. The poles are located in the point spectrum of the associated tridiagonal infinite matrix and their order determined in terms of the asymptotic behavior of the zeros of the denominators of the corresponding partial fractions. Sponsor: Research by second author (G.L.L.) partially supported by RG-297 Maths/LA from Third World Academy of Science. Review: PeerReviewed Publisher version: http://dx.doi.org/10.1006/jath.1998.3165 Keywords: Continued fractionsJ-fractionsTridiagonal infinite matricesAsymptotic behaviour of poles Rights: © Elsevier Appears in Collections: DM - GAMA - Artículos de Revistas

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