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Feb 27, 2016 at 17:12 comment added Sebastian Goette @BenMcKay You are right. I was somehow automatically thinking of $L^2$ sections, even though this was not demanded.
Feb 27, 2016 at 16:41 comment added Ben McKay For a more elementary example of infinite dimensional kernel on noncompact manifolds, you could just look at the kernel of the Cauchy Riemann operator on complex functions of one complex variable.
Feb 27, 2016 at 16:32 history answered Sebastian Goette CC BY-SA 3.0