A note on three conjectures by Gonchar on rational approximation (Q1097430)

The results of this paper have been announced in a preprint of the Technical University Berlin (1985). The main one is the proof of a generalization of a conjecture by A. A. Gonchar on the asymptotics of the order of approximation by rational functions of degree n (nth diagonal Padé approximants) [in the paper read v(f-r) instead of v(f,r)]; log- capacity plays a role. Two other theorems partially prove other conjectures, connected with the asymptotic behaviour of the constant of best-rational approximation on sets where the function is analytic (here plane condensor capacity plays an important role).