CONDITIONS FOR ABSOLUTE CONVERGENCE OF THE TAYLOR COEFFICIENT SERIES OF A MEROMORPHIC FUNCTION OF 2 VARIABLES

It is proved that the Taylor series of a meromorphic function of two v ariables converges absolutely in the closed unit bidisk U2BAR if this function satisfies a Holder condition in U2BAR with exponent 1/2, whil e for any epsilon > 0 there exists a rational function with Holder exp onent 1/2 - epsilon such that the indicated series diverges. This resu lt solves the problem of stability of two-dimensional recursive digita l filters. In its proof the structure of the asymptotic behavior of th e Taylor coefficients of a meromorphic function of two variables is in vestigated.