Timeline for Spectral properties of Non-local Differential operators on real line
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| S Feb 6, 2018 at 18:48 | history | bounty ended | CommunityBot | ||
| S Feb 6, 2018 at 18:48 | history | notice removed | CommunityBot | ||
| S Jan 29, 2018 at 17:16 | history | bounty started | mystupid_acct | ||
| S Jan 29, 2018 at 17:16 | history | notice added | mystupid_acct | Authoritative reference needed | |
| Jan 26, 2018 at 16:01 | comment | added | SetHead | For strongly singular kernels, see Theorem 2.5 of "Reaction-diffusion equations with fractional diffusion on non-smooth domains with various boundary conditions" by Gal and Warma in DCDS (2016), especially see their reference [48], which in turn relies "Heat Kernels and Spectral Theory" by on E.B. Davies, Cambridge University Press, Cambridge (1989). | |
| Jan 26, 2018 at 9:10 | comment | added | mcd | To push this more into the microlocal (ie pseudodifferential) direction: If $K(x,y) = \int e^{i(x-y)\xi} |\xi|^2 d\xi$ you get again (modulo constants) the Laplacian, so for arbitrary kernels you cannot treat $K$ as a small perturbation. So you need to add some condition on the regularity of $K$. | |
| Jan 26, 2018 at 1:22 | comment | added | paul garrett | It seems to me that a sane framework for such issues is that of pseudo-differential operators, or possibly Fourier integral operators. In both cases, there is a substantial body of existing work. But if by "Sturm-Liouville theory" you mean an implicit assertion that the spectrum (in whatever useful sense) is discrete, you are surely doomed to be frustrated in any general situation, because even the simplest examples can have continuous spectrum... | |
| Jan 25, 2018 at 23:05 | comment | added | Igor Khavkine | A more common name for these kind of operators/equations is integro-differential. | |
| Jan 25, 2018 at 16:43 | history | edited | mystupid_acct | CC BY-SA 3.0 |
Added definition of non-local PDE
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| Jan 25, 2018 at 16:37 | comment | added | mystupid_acct | ok, I add a definition. | |
| Jan 25, 2018 at 16:30 | comment | added | Denis Serre | You won't get answers, unless you explain what you means by non-local. Notions of non-something are vague. You can have a precise idea of what you mean, while nobody shares your understanding. | |
| Jan 25, 2018 at 16:22 | history | edited | mystupid_acct | CC BY-SA 3.0 |
added 128 characters in body; edited title
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| Jan 24, 2018 at 22:59 | history | edited | mystupid_acct | CC BY-SA 3.0 |
added 153 characters in body
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| Jan 24, 2018 at 22:45 | history | asked | mystupid_acct | CC BY-SA 3.0 |