Timeline for Rigorous justification for this formal solution to $f(x+1)+f(x)=g(x)$

7 events

when toggle format	what		by	license	comment
Jun 24, 2019 at 19:31	history	edited	Carlo Beenakker	CC BY-SA 4.0	edited body
Jun 24, 2019 at 15:36	comment	added	Will Sawin		@NeilStrickland One thing this argument should show is that there is a unique solution in the space of distributions whose Fourier transforms are supported in some region $U$ of the plane that does not contain $\pi n$ for $n$ odd. In particular, there is a unique solution in distributions whose Fourier transform is supported at the origin. But this may be nothing more than the (obvious from linear algebra) that there is a unique polynomial solution.
Jun 24, 2019 at 15:30	comment	added	Neil Strickland		So what exactly is your conclusion? Your exposition suggests that there is a unique solution in some unspecified space, but as mentioned in the original question, that will fail if the candidate space contains $\sin(\pi x)$.
Jun 24, 2019 at 15:17	history	edited	Carlo Beenakker	CC BY-SA 4.0	added 65 characters in body
Jun 24, 2019 at 15:11	history	edited	Carlo Beenakker	CC BY-SA 4.0	added 231 characters in body
Jun 24, 2019 at 15:03	history	edited	Carlo Beenakker	CC BY-SA 4.0	added 15 characters in body
Jun 24, 2019 at 14:57	history	answered	Carlo Beenakker	CC BY-SA 4.0