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created pullback of a distribution, just for completeness
added statement of a second sufficient condition for the pullback of distributions to exist: their wave front set does not intersect the conormal bundle of the map being pulled back along: here
Oh, here I see what I was talking in another entry. The formula for pullback has Jacobianâ€¦this is exactly because Hoermander takes generalized 1-densities and not generalized functions in geometric sense. For generalized functions as functionals on classical distributions (1-densities), no conditions for pullback.
Wait a second. I was wrong in 3. To pushforward the test 1-density as a measure no problem but you can loose smoothness if it is not a submersion. Thus the condition that one needs submersion if one wants to pullback all generalized functions.
added to pullback of distributions the example of restrictions of distributions: here
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