= Spectral Tikhonov differentiation for the Volterra operator
{c}
{title2=$x_\alpha=\sum_n\frac{a_n}{1+\alpha a_n^2}\langle y,v_n\rangle u_n$}
The <Tikhonov regularization> of the <Volterra integration operator> replaces the unbounded differentiation gain $a_n$ by $a_n/(1+\alpha a_n^2)$. The series converges in $L^2$ for every datum and $\alpha>0$. On the <range of the Volterra integration operator>, it converges to the <weak derivative> of the datum as $\alpha\downarrow0$. No pointwise differentiation of arbitrary noisy <L2 space> data is required.
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