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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTime6 days ago
    • (edited 6 days ago)

    I want to be adding some details to Cauchy principal value. What’s a good reference? Say for the proof that up to addition of a delta-distribution, f(x)=pv(1x)f(x) = pv\left( \frac{1}{x}\right) is the unique distributional solution to xf=1x f = 1?

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTime6 days ago
    • (edited 6 days ago)

    okay, I have added some content to Cauchy principal value.

    (Still lacking, though, the proof that PV(1/x)+cδ(x)PV(1/x) + c \delta(x) is the most general solution to xf(x)=1x f(x) = 1.)

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTime4 minutes ago

    Still lacking, though, the proof that

    Ah, that follows of course immediately with the characterization of extension of distributions to the point.

    I have also cross-linked now with step function, in fact I copied over the computation from there to Cauchy principal value: here