On the Problem of Describing Sequences of Best Trigonometric Rational Approximations

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