\gamma(s)|=1$. In view of the smoothness assumption the curve possesses locally Frenet’s frame, i.e. the triple $(t(s),b(s),n(s))$ of the tangent, binormal and normal vectors; we assume its global existence[^5]. For a fixed nonzero $\rho \in {\mathbb{R}}^2$ we define the “shifted” curve $\Gamma_{\rho}$ as the graph of the function $$\gamma_{\rho}(s)):=\gamma(s)+\rho_1 b(s)+\rho_2 n(s)\,;$$ the distance between the two is obviously $r:=|\rho|$. If we suppose in addition that $\Gamma$ does not have “near-intersections” as in Sec. \[ss: regular\] then clearly $\Gamma_{\rho}\cap \Gamma =\emptyset$ holds provided $r$ is small enough. Since any function $f\in W_{loc}^{2,2}({\mathbb{R}}^{3}\setminus
\Gamma )$ is continuous on ${\mathbb{R}}^{3}\setminus \Gamma$ its restriction to $\Gamma_{\rho}$ is then well defined; we denote it as ${f\big|}_{\Gamma_{\rho}}$, in fact, we can regard ${f\big|}_{\Gamma_{\rho}}$ as a distribution from $D^{\prime}({\mathbb{R}})$ with the parameter $\rho$. We denote by ${\mathcal{D}}$ the set of functions $f\in W_{loc}^{2,2}({\mathbb{R}}^{3}\setminus \Gamma )\cap L^{2}({\mathbb{R}}^{3})$ such that the following limits $$\begin{aligned}
 \Xi (f)(s) &\!:=\!& -\lim_{r \to 0}\frac{1}{\ln r }
 {f\big|}_{\Gamma_{\rho}}(s)\,, \\
 \Omega (f)(s) &\!:=\!& \lim_{r \to 0}
 {f\big|}_{\Gamma_{\rho}} (s)+\Xi (f)(s)\ln r\,,
 \end{aligned}$$ exist a.e. in ${\mathbb{R}}$, are independent of the direction ${1\over
r}\rho$, and define functions from $ L^{2}({\mathbb{R}})$; the limits here are understood in the sense of the $D^{\prime }({\mathbb{R}})$ topology. Now we are able 