On the problem of uniqueness of the trigonometric moment constants

Summary Given a real-valued function ]]>]]>]]>]]>]]>]]>]]>mu(x,y)$ of bounded variation in the sense of Hardy and Krause on the square $[0, 2pi]times [0, 2pi]$, the sequence ]]> mu_{m,n}:=int^{2pi}_0 int^{2pi}_0 e^{i(mx+ny)} , d_x , d_y mu(x,y), quad (m,n)in bZ^2, $$ may be called the sequence of trigonometric moment constants with respect to $mu(x,y)$. We discuss the uniqueness of the expression of the sequence ${mu_{m,n}}$ in terms of the function $mu(x,y)$.