Equiconvergence in rational approximation of meromorphic functions (Q1123322)

The result of \textit{E. B. Saff}, \textit{A. Sharma} and \textit{R. S. Varga} [RAIRO, Anal. Numér. 15, 371-390 (1981; Zbl 0485.41003)] is extended in the same manner as the theorem of \textit{A. S. Cavaretta}, \textit{A. Sharma} and \textit{R. S. Varga} [Result. Math. 3, 155-191 (1981; Zbl 0447.30020)] generalizes Walsh's theorem on equiconvergence. The rate of equiconvergence of rational interpolants in the roots of unity and of the introduced rational interpolants coincides with one from Cavaretta's, Sharma's and Varga's theorem. The correctness of the definition of the introduced rational interpolants for a class of meromorphic functions is proved.