Timeline for The origin of Discrete `Liouville's theorem'

8 events

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Dec 13, 2019 at 9:53	comment	added	Seva		Rather off-topic, but I wonder whether it is possible to prove Liouville's theorem considering a function like $F(x,y)=\sum_{i,j} f(i,j) x^iy^j$. (As written, this does not make much sence, of course, since the series diverges.) We then have $$ 4F(x,y) = \sum_{i,j} \left(xf(i-1,j)x^{i-1}j+\dotsb+\frac1yf(i,j+1)x^iy^{j+1} \right) $$ whence $4F(x,y)=(x+1/x+y+1/y)F(x,y)$, implying $F(x,y)=0$.
Jan 9, 2019 at 16:32	history	edited	Carlo Beenakker	CC BY-SA 4.0	Http to https
Jan 3, 2014 at 0:09	history	bounty ended	Alexey Ustinov
Jan 3, 2014 at 0:05	vote	accept	Alexey Ustinov
Dec 31, 2013 at 12:52	comment	added	Alexey Ustinov		If I understood correctly, one of Capoulade's proofs is based on a result by La Roux, who gave explicit formula for the solution of Dirichlet problem in rectangle. The last article is available in Gallica, see portail.mathdoc.fr/JMPA/…
Dec 31, 2013 at 12:34	comment	added	Alexey Ustinov		Dear Carlo, thank you very much for the article. It is at least a half of an answer. Probably Capoulade was the first who had proved this theorem.
Dec 31, 2013 at 12:25	history	edited	Carlo Beenakker	CC BY-SA 3.0	added 111 characters in body
Dec 31, 2013 at 12:16	history	answered	Carlo Beenakker	CC BY-SA 3.0