the function r − 1 n I ( B$_{n}$ ) exp (Λ( ζ )) ψ ( ζ ) is bounded . It is then sufficient to find B$_{n}$ such that r − 1 n I ( B$_{n}$ ) exp (Λ( ζ )) is bounded (by possibly a polynomial), thus it is sufficient that sup B n | exp (Λ( ζ )) r − 1 n | be bounded. This will hold if exp ( ¯ B k n ) < r$_{n}$, ¯ B k n < ln r$_{n}$. ■ 

Of course an even slower growth for spectral cut-off would result from Λ that grows faster than a polynomial. The consequence of the slow growth of the support is usually a correspondingly slow rate of convergence for φ − 1 u ε$_{n}$I ( B$_{n}$ ) . Additional conditions (as in function spaces) are needed for the regularized estimators to converge to the true γ . 

It may be advantageous to focus on lower frequency components and ignore the contribution from high frequencies when the features of interest depend on the contribution at low frequency. 

## 6 Concluding remarks 

Working in spaces of generalized functions extends the results on nonpara- metric identification and well-posedness for a wide class of models. Here identification in deconvolution is extended to generalized densities in the class of all distributions from the usually considered classes of integrable den- sity functions. In regression with Berkson error nonparametric identification in S ∗ holds for functions of polynomial growth, extending the usual results obtained in L$_{1}$ ; a similar extension applies to regression with measurement error and Berkson type measurement; this allows to consider binary choice 

