Geodesic
Conditions for absolute convergence of the Taylor coefficient series of a meromorphic function of two variables
Sbornik. Mathematics, Tome 74 (1993) no. 2, pp. 337-360 
A. K. Tsikh. Conditions for absolute convergence of the Taylor coefficient series of a meromorphic function of two variables. Sbornik. Mathematics, Tome 74 (1993) no. 2, pp. 337-360. http://geodesic.mathdoc.fr/item/SM_1993_74_2_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the Taylor series of a meromorphic function of two variables converges absolutely in the closed unit bidisk $\overline U^2$ if this function satisfies a Hölder condition in $\overline U^2$ with exponent $1/2$, while for any $\varepsilon>0$ there exists a rational function with Hölder exponent $1/2-\varepsilon$ such that the indicated series diverges. This result solves the problem of stability of two-dimensional recursive digital filters. In its proof the structure of the asymptotic behavior of the Taylor coefficients of a meromorphic function of two variables is investigated.

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