On the Problem of Describing Sequences of Best Trigonometric Rational Approximations

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