Distribution of interpolation points of maximally convergent multipoint Pade approximants

作者：Blatt H P^*; Kovacheva R K

来源：Journal of Approximation Theory, 2015, 191: 46-57.

DOI：10.1016/j.jat.2014.04.004

• Pade approximation
• m(1)-maximal convergence

The paper investigates the distribution of interpolation points of m(1)-maximally convergent multipoint Pade approximants with numerator degree <= n and denominator degree <= m(n) for meromorphic functions f on a compact set E subset of C, where m(n) = o(n/log n) as n -> infinity. It is shown that the normalized counting measures (resp. their associated balayage measures onto the boundary of E) converge for a subsequence in the weak* sense to the equilibrium measure mu(E) of E if the multipoint Pade approximants for one single function f converge exactly in m(1)-measure on the maximal Green domain of meromorphy E-rho(f).

• 出版日期2015-3