Can any function of two variables be expressed as a linear combination (may be infinite) of a product of two single-variable functions?
$f(x,y) = \sum A_n g_n(x) h_n(y)$
Asked
Active
Viewed 63 times
3
-
You should lookup Taylor's formula in two variables. – PierreCarre Jan 14 '21 at 14:23
-
I believe there is no general answer. See this MathOverflow question: When is separation of variables an acceptable assumption to solve a PDE? – Jan 14 '21 at 14:23
-
@PierreCarre Not all functions are analytical somewhere. – Kandinskij Jan 14 '21 at 14:25
-
@Eureka sure... I'm just saying that the statement can be proven correct for some class of functions. – PierreCarre Jan 14 '21 at 14:28
-
It's true for at least continuous function (and I think for Borel functions too). – mihaild Jan 14 '21 at 21:06