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nLab > Latest Changes: compactly supported distribution

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 18th 2017
    • (edited Oct 18th 2017)

    added statement and proof that compactly supported distributions are equivalently the smooth linear functionals: here

    (in the sense of either diffeological spaces, or smooth sets, or formal smooth sets/Cahiers topos).

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 23rd 2017
    • (edited Oct 23rd 2017)

    I have spelled out here the characterization of continuity of a linear map u:C∞(ℝn)→ℝ as in Hörmander’s book

    ∃K,k,C(|u(Φ)|≤C∑|α|≤ksupx∈K|∂αK|)

    from the un-summed seminorms Φ↦supx∈K|∂αΦ(x)|.

  3. 1) semi-norms giving the inductive limit definition of \mathcal{E}(\Omega) should be defined on C^\infty functions, not only on test functions.

    2) typo in the the math font for one name of \mathcal{E}

    lucas

    diff, v21, current

  4. 1) confusion between bump functions and smooth functions

    2) the defined semi-ball (of smooth functions) was in R^n

    lucas

    diff, v21, current

1 to 4 of 4

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