Fourier-Haar coefficients and properties of continuous functions.

It is well known that if the Fourier-Haar coefficients have a certain order or if a certain series composed of the Fourier-Haar coefficients of a function f( x) ∈ C(0, 1) converges, then the function has a certain form. In the present paper, we prove that not only the Fourier-Haar coefficients, but also the difference of these coefficients possess these properties. [ABSTRACT FROM AUTHOR]