Timeline for Smooth algebraic functions

8 events

when toggle format	what		by	license	comment
Dec 7, 2014 at 5:36	vote	accept	BigM
Dec 7, 2014 at 5:30	history	edited	BigM	CC BY-SA 3.0	Corrections
Dec 7, 2014 at 5:26	answer	added	Alexandre Eremenko		timeline score: 4
Dec 7, 2014 at 4:15	history	edited	BigM	CC BY-SA 3.0	Corrections
Dec 7, 2014 at 4:15	comment	added	Lev Borisov		I think if you have convergence for all $x$ in $\mathbb R^n$, you will have bounds on the coefficients that would make it absolutely convergent for all $x$ in $\mathbb C^n$. An algebraic function will have at most polynomial growth, so Cauchy's theorem should imply that high degree coefficients vanish.
Dec 7, 2014 at 4:10	comment	added	BigM		Algebraic function in this sense.
Dec 7, 2014 at 3:49	comment	added	John Pardon		What do you mean by algebraic? Algebraic over the ring of polynomial functions on $\mathbb R^n$?
Dec 7, 2014 at 2:23	history	asked	BigM	CC BY-SA 3.0