Timeline for If $f(x_1,x_2)=f(x_2,x_1)$, $f(x_1,x_2)=\sum_k \lambda_k f_k(x_1)f_k(x_2)$? [closed]

9 events

when toggle format	what		by	license	comment
Dec 20, 2019 at 17:07	history	closed	Francois Ziegler user44191 ARG Max Horn Alex M.		Needs details or clarity
Dec 19, 2019 at 12:40	review	Close votes
Dec 20, 2019 at 17:07
Dec 19, 2019 at 12:20	comment	added	Francois Ziegler		In what sense is the series’ convergence supposed to be?
Dec 19, 2019 at 12:03	answer	added	Iosif Pinelis		timeline score: 5
Dec 19, 2019 at 11:38	comment	added	Mateusz Kwaśnicki		If $f$ is the kernel of, say, a Hilbert–Schmidt operator on $L^2(dm)$, then of course yes. In general, the answer depends on your notion of convergence of the series, but most likely it is "not necessarily". If I am not mistaken, $m(dx) = e^{-x^2} dx$ and $f(x,y) = e^{x^2+y^2}$ is a simple counter-example under reasonable notions of convergence.
Dec 19, 2019 at 10:02	comment	added	mathmetricgeometry		@BenMcKay: The conditions given above show that it's square integrable
Dec 19, 2019 at 9:37	comment	added	Ben McKay		Do you want these $f_k$ to be square integrable functions?
Dec 19, 2019 at 9:34	comment	added	Anthony Quas		Ummm. Are there any hypotheses you’d like us to know about?
Dec 19, 2019 at 8:43	history	asked	mathmetricgeometry	CC BY-SA 4.0