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1. • CommentRowNumber1.
   • CommentAuthorTodd_Trimble
   • CommentTimeFeb 14th 2018
   • (edited Feb 14th 2018)
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   Author: Todd_Trimble
   Format: MarkdownItexTook a stab at a general formulation of [[Poisson summation formula]], although the class of functions to which it is supposed to apply wasn't nailed down (yet). (Some of the ingredients of Tate's thesis are currently on my mind.)

   Took a stab at a general formulation of Poisson summation formula, although the class of functions to which it is supposed to apply wasn’t nailed down (yet).

   (Some of the ingredients of Tate’s thesis are currently on my mind.)

2. • CommentRowNumber2.
   • CommentAuthorDavidRoberts
   • CommentTimeFeb 14th 2018
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexI guess the part with $f(a+c)$ really means: push forward $f$ by integrating over the $A$-cosets, then integrate over $C$? The measure on $A$ must give a family of measures on the fibres.

   I guess the part with $f(a+c)$ really means: push forward $f$ by integrating over the $A$-cosets, then integrate over $C$? The measure on $A$ must give a family of measures on the fibres.

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeFeb 14th 2018
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   Author: Todd_Trimble
   Format: MarkdownItexYes, thanks; it could be made clearer along those lines. I'll do a fix-up later.

   Yes, thanks; it could be made clearer along those lines. I’ll do a fix-up later.

4. • CommentRowNumber4.
   • CommentAuthorTodd_Trimble
   • CommentTimeFeb 16th 2018
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   Author: Todd_Trimble
   Format: MarkdownItexAlong with the fix-up, I finally filled in some missing elements in [[Poisson summation formula]], in particular the general notion of a [[Schwartz-Bruhat function]] (new entry) which plays the same role for general locally compact abelian groups that Schwartz functions play for Euclidean spaces. I found it pretty difficult to extract that notion from the literature, because some of the relevant authorities seem a bit cavalier when they invoke categorical language as to what they're doing exactly. I have some confidence that what I wrote down is correct, but I'm going to have to sleep on it some more. The theory Bruhat develops does seem elegant though.

   Along with the fix-up, I finally filled in some missing elements in Poisson summation formula, in particular the general notion of a Schwartz-Bruhat function (new entry) which plays the same role for general locally compact abelian groups that Schwartz functions play for Euclidean spaces.

   I found it pretty difficult to extract that notion from the literature, because some of the relevant authorities seem a bit cavalier when they invoke categorical language as to what they’re doing exactly. I have some confidence that what I wrote down is correct, but I’m going to have to sleep on it some more. The theory Bruhat develops does seem elegant though.