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Dec 21, 2022 at 12:09 vote accept Isaac
Dec 21, 2022 at 12:09 comment added Isaac I see. I guess the IR cutoff (or behavior at infinity) is somehow related to the average to $0$, which is the crucial property.. Thank you for your answer.
Dec 21, 2022 at 9:51 comment added Martin Hairer Makes no difference, the problem isn't the behaviour of the test functions at infinity, but whether they average to $0$ or not.
Dec 21, 2022 at 3:57 comment added Isaac Thank you for your answer. I would like to make it a "normal" distribution, not necessarily tempered. Then the issue is whether or not the 2D GFF makes sense directly when testing against compactly supported smooth functions only. More concretely, I am concerned about the integral at the bottom of my question. Could you please help me evaluate it?
Dec 20, 2022 at 22:56 history answered Martin Hairer CC BY-SA 4.0