Weighted maximum over minimum modulus of polynomials, applied to ray sequences of Pade approximants

Let a greater than or equal to 0, epsilon > 0. We use potential theory to obtain a sharp lower bound for the linear Lebesgue measure of the set [GRAPHICS] Here P is an arbitrary polynomial of degree less than or equal to n. We then apply this to diagonal and ray Pade sequences for functions analytic (or meromorphic) in the unit ball. For example, we show that the diagonal {[n/n]}(n=1)(infinity), sequence provides good approximation on almost one-eighth of the circles centre 0, and the {[2n/n]}(n=1)(infinity) sequence on almost one-quarter of such circles.