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Sep 29, 2013 at 20:40 comment added user36539 @Kofi Computer scientists prefer high level language (C, Pascal) than Assembler contrary to the situation for (pure) mathematicians which preffer "assembler-like" language...If you preffer Laplacian given on sections of TS viewed as a Hilbert space of half-densities $L^2(S)$
Sep 29, 2013 at 20:32 comment added user36539 Laplacian given on the sphere S, its domain is a dense subset of $L^2(S)$ but its resolvent is compact...Obviously the Laplacian acts on function belonging to $L^2(S)$ which take values on the sphere
Sep 29, 2013 at 17:13 comment added Matthias Ludewig An unbounded operator "on" a compact manifold does not even make sense, although I can imagine what you mean. However, this is merely some example, and the question was way more general.
Sep 27, 2013 at 18:18 history answered user36539 CC BY-SA 3.0