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to zero. From the nature of the identified solution (9) or (10) it follows that if it can be shown that ε − 1 1 η$_{·}$$_{,n}$ converges to zero then the problem for the distribution of the latent factor is well-posed. But this is indeed the case since the exponents cancel, ¯ η$_{·}$$_{,n}$ converges to zero in S ′ and convergence to zero follows by hypocontinuity of the product ¯ ε − 1 1 ¯ η$_{·}$$_{,n}$ . 

The values for the tail exponent have to be fixed implying that even a slight deviation in the exponent violates the well-posedness condition: there are no two different Gaussian distributions in the class. Since an estimated Gaussian will differ from the true Gaussian they cannot belong to the same non-parametric class thus there is separation between estimation in the para- metric Gaussian problem and in the fully general nonparametric specification in S $^{′}$. 

Consider a solution regularized with a weighting function. It is high frequency components that cannot be identified in convolution with a su- per smooth function and regularization smooths those out. Fix a function ψ ∈ D. Using this weight on the Fourier transform is equivalent to solving convolution equations 

<img src='content_image/323613.jpg'>

As in the proof of Theorem 3 of Zinde-Walsh 2010 for any such ψ the solution exists because multiplication by a continuous function γ − 1 or φ − 1 

