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 if this function satisfies a Holder condition in with exponent , while for any there exists a rational function with Holder exponent 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.