SmoothnessOperator ill-posedness
Visualizing nifty's SmoothnessOperator smoothingoperator.pdf over some PowerSpace, I was wondering whether having no penalty on the highest frequency entry (indicated by the empty last row and column in the attached picture) is the desired behavior?
I understand that this might be desired for the zero mode (and maybe the next one too) since the data should be informative enough to render the overall problem well-posed. But for the highest frequency mode, I would expect heavy problems in optimization from leaving this degree-of-freedom basically free.