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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeAug 6th 2017

created pullback of a distribution, just for completeness

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeAug 7th 2017

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

• CommentRowNumber3.
• CommentAuthorzskoda
• CommentTimeAug 8th 2017

Oh, here I see what I was talking in another entry. The formula for pullback has Jacobian…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.

• CommentRowNumber4.
• CommentAuthorzskoda
• CommentTimeAug 8th 2017
• (edited Aug 8th 2017)

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.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeAug 11th 2017

added to pullback of distributions the example of restrictions of distributions: here

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeDec 27th 2017
• (edited Dec 28th 2017)

added characterization of the wave front set of the pullback of a distribution: here

[edit: fixed]

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