# Conservation of compactness

Gold Member
Hi PF

I have an operator in the set of indefinitely derivable functions on R^4.
How can we caracterize the operators which send f with supp f compact to a function with compact support?
My example uses the Klein Gordon operator K an its green's function adv and ret.
let us take f such that ##g_1 = \int ret. f ## and ##g_2 = \int adv. f##
K sends g1 to f and ret sends K(g1) to g2
does g1 -> g2 conserves compactness of supports?
thanks

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