The convergence of diagonal Padé approximants and the Padé conjecture
The Baker-Gammel-Wills conjecture says that if the function \(f\) is meromorphic in the unit disc \(D\), then there exists an infinite subsequence of diagonal Padé approximants \([n/n]\) converging to \(f\) locally uniformly in \(D\{\)poles of \(f\)\}. The author formulates some special and weaker versions of the above conjecture and analyses the role played by ``spurious poles'' of the approximants, i.e. poles of \([n/n]\) that do not correspond to poles of \(f\). Two types of convergence is considered: locally uniform convergence and convergence in capacity.
scientific article; zbMATH DE number 1115938
scientific article