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nLab > Latest Changes: convolution product of distributions

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 2nd 2017

    started some minimum at convolution product of distributions

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 28th 2017
    • (edited Nov 28th 2017)

    added this statement (here and also at wave front set here):

    Let u,v∈ℰ′(ℝ n)u,v \in \mathcal{E}'(\mathbb{R}^n) be two compactly supported distributions. Then the wave front set of their convolution of distributions is

    WF(u⋆v)={(x+y,k)|(x,k)∈WF(u)and(y,k)∈WF(u)}. WF(u \star v) \;=\; \left\{ (x + y, k) \;\vert\; (x,k) \in WF(u) \,\text{and}\, (y,k) \in WF(u) \right\} \,.

  3. I checked the hormander textbook, the definition contains an error, the function convoluted with the tempered distribution has to be smooth and with compact support.

    Daniele Zerbini

    diff, v7, current

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