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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
I gave product of distributions its own entry. For the moment it just points to the definition in Hörmander’s book.
This should eventually supercede the section “Multiplication of distributions” at distributions, which I find suboptimal: that section starts very vaguely referring to physics as if the issue only appears there, and it keeps being very vague, with its three sub-subsections being little more than a pointer to one reference by Colombeau.
I suggest to
remove that whole subsection at distribution and leave just a pointer to product of distributions
move the mentioning of Colombeau’s reference to product of distributions and say how it relates to Hörmander’s definition
remove all vague mentioning of application in physics and instead add a pointer to Wick algebra and microcausal functional, which I will create shortly.
Since nobody objected to the suggestion #1, I went ahead and implemented it. Details on what I did are here.
I have spelled out the definition of the product of distributions with compatible wave front sets (from Hörmander 90) and the proof that this is well defined: here.
That proof however relies on a little hierarchy of lemmas. I have added statement (not the proof yet, but pointers to Hörmander’s proofs) of the next lower lemmas at tensor product of distributions and at pullback of distributions.
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