RT Journal Article
T1 On the domain of convergence and poles of complex J-fractions
A1 Barrios, Dolores
A1 López Lagomasino, Guillermo
A1 Martínez-Finkelshtein, Andrei
A1 Torrano, Emilio
AB 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.
PB Elsevier
SN 0021-9045
YR 1998
FD 1998-05
LK https://hdl.handle.net/10016/6367
UL https://hdl.handle.net/10016/6367
LA eng
NO 24 pages, no figures.-- MSC2000 code: 30B60.
NO MR#: MR1616769 (99b:30003)
NO Zbl#: Zbl 0909.30002
NO Research by second author (G.L.L.) partially supported by RG-297 Maths/LA from Third World Academy of Science.
DS e-Archivo
RD 3 ago. 2024