The authors study the behaviour of the alternation (equioscillation) points for the error in best uniform rational approximation of an
. The theorems proved here may be compared with some known results for best polynomial approximation given by some of these authors and some others [see A. Kroo
and E. B. Saff
, Proc. Am. Math. Soc. 103, No.1, 203-209 (1988; Zbl 0663.41027
)]. They give three theorems. From the first theorem, in the context of Walsh table they deduce that these points are dense in the interval [-1,1] if one goes down the table along a ray above the main diagonal. In Theorem 2 they provide a result similar to one due to M. I. Kadec
[Usp. Mat. Nauk 15, No.1(91), 199-202 (1960; Zbl 0136.364
)] on polynomial approximations. In the third theorem they furnish a counter example to show that the result may not be true for a subdiagonal of the table.