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On the Domain of Convergence and Poles of ComplexJ-Fractions

✍ Scribed by D Barrios Rolanı́a; G López Lagomasino; A Martı́nez Finkelshtein; E Torrano Giménez

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
329 KB
Volume
93
Category
Article
ISSN
0021-9045

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✦ Synopsis

Consider the infinite J-fraction

we prove that this continued fraction converges to a meromorphic function in C"R. Such conditions hold, in particular, if lim n J(a n )=lim n J(b n )=0 and

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.

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