Conditions for absolute convergence of the Taylor coefficient series of a meromorphic function of two variables

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.