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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, $f(x) = pv\left( \frac{1}{x}\right)$ is the unique distributional solution to $x f = 1$?

• 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 $PV(1/x) + c \delta(x)$ is the most general solution to $x f(x) = 1$.)

• 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