Timeline for Analytic hypoellipticity of linear ordinary differential operators
Current License: CC BY-SA 2.5
8 events
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| Sep 24, 2010 at 19:56 | history | edited | Deane Yang | CC BY-SA 2.5 |
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| Sep 24, 2010 at 19:54 | comment | added | Deane Yang | My apologies. I didn't realize you needed this for a paper. All too late, I understand your request and frustration. When I've encountered similar situations in the past, I've included a statement and proof in a short appendix to my paper. | |
| Sep 24, 2010 at 13:59 | comment | added | Armin Straub | Because it's for a paper where this is a technical detail: a function f(x) which is not known to be smooth (and in fact isn't everywhere) has a Mellin transform which satisfies a functional equation. By the distributional Mellin formulation it follows that f(x) is the weak solution of a differential equation. To conclude that f(x) is analytic on certain intervals, we currently appeal to elliptic regularity. While that certainly works (and is just one sentence plus reference) it feels a bit overpowered for the case of an ODE. | |
| Sep 24, 2010 at 12:52 | comment | added | Deane Yang | But I don't understand why you think that one sentence should suffice. | |
| Sep 24, 2010 at 12:51 | history | edited | Deane Yang | CC BY-SA 2.5 |
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| Sep 24, 2010 at 11:21 | comment | added | Deane Yang | But my proof does not use any elliptic theory at all. It is merely based on it. | |
| Sep 24, 2010 at 5:37 | comment | added | Armin Straub | Probably I didn't phrase the question well enough: For an audience which may not be familiar with the theory of elliptic operators, what would be the proper way to (in one sentence plus a reference) justify that a weak solution in the case at hand is automatically real analytic? Currently, I have to make reference to a textbook on PDEs which treats elliptic regularity even though the problem for linear ODEs seems so much simpler. I very much appreciate your nice outline though! | |
| Sep 24, 2010 at 1:26 | history | answered | Deane Yang | CC BY-SA 2.5 |