The Fourier coefficients of functions with bounded variation

We consider Fourier coefficients for functions of bounded variation with respect to general orthonormal systems (GONS). We show that in general case the sequence of coefficients may have an arbitrarily prescribed order of vanishing. In this connection we seek for a class of GONS such that Fourier coefficients of a function from V (0, 1) satisfy the same inequality as in the case of classical systems (trigonometric, Walsh, and Haar ones). In the present paper we study this problem and related issues.