I'm curious about differential Galois theory and I've noticed that everything I read covers only finite order operators (e.g. $L = Y^n + a_{n-1} Y^{n-1} + \dots + a_0 Y$). Has there been any work on using differential Galois theory to instead study infinite operators?
$\begingroup$
$\endgroup$
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
2
The March 2010 paper by Bernard Malgrange, Pseudogroupes de Lie et théorie de Galois différentielle, IHES/M/10/11 https://hal.archives-ouvertes.fr/hal-00469778 covers this case, I believe.
-
$\begingroup$ Sadly, Malgrange passed away a few days ago. $\endgroup$– M.G.Commented Jan 12 at 2:10
-
1$\begingroup$ @M.G. Sad news indeed. A relevant lecture for us to remember him by: youtu.be/EWQJx1RxiBw?si=ErclEiulcn6_zspT $\endgroup$ Commented Jan 15 at 1:16