Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: pullback of a distribution

Bottom of Page

1 to 6 of 6

  1.  
    • 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]

1 to 6 of 6

  1.