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

For a fixed sequence $\{a_n\}^\infty_{n=0}$ of non-negative real numbers strictly decreasing to zero a continuous $2\pi$-periodic function $f$ is constructed such that $R^T_n(f)=a_n$, $n=0,1,2,\dots$, where the $R^T_n(f)$ are the best approximations of $f$ in the uniform norm by rational trigonometric functions of degree at most $n$.