  Wavelet transform has been attracting attention as a tool for regularization
of gauge theories since the first paper of (Federbush, Progr. Theor. Phys. 94,
1135, 1995), where the integral representation of the fields by means of the
wavelet transform was suggested: $$A_{\mu}(x) = \frac{1}{C_\psi} \int_{\R_+
\times\R^d} \frac{1}{a^d} g \left(\frac{x-b}{a} \right) A_{\mu a}(b)
\frac{dad^db}{a},$$ with $A_{\mu a}(b)$ being understood as the fields $A_\mu$
measured at point $b\in \R^d$ with resolution $a\in\R_+$. In present paper we
consider a wavelet-based theory of gauge fields, provide a counterpart of the
gauge transform for the scale-dependent fields: $A_{\mu a}(x)\to A_{\mu
a}(x)+\d_\mu f_a(x)$, and derive the Ward-Takahashi identities for them.
