On the problem of the description of sequences of best rational trigonometric approximations

For a fixed sequence {alpha(n)}(n=0)(infinity) of non-negative real numbers strictly decreasing to zero a continuous 2 pi-periodic function f is const ructed such that R-n(T)(f) = alpha(n), n = 0, 1, 2,..., where the R-n(T) (f ) are the best approximations of f in the uniform norm by rational trigonom etric functions of degree at most n.