Timeline for Literature on behaviour of eigenfunctions under multiplication?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 26, 2011 at 11:39 | comment | added | herrsimon | @Gil: Maybe it is, but this is not what I had in mind when posing the question | |
| Aug 26, 2011 at 10:49 | comment | added | Gil Kalai | Is the question related to expansions of products of representations in terms of irreducible ones? | |
| Aug 26, 2011 at 9:35 | vote | accept | herrsimon | ||
| Aug 26, 2011 at 9:35 | vote | accept | herrsimon | ||
| Aug 26, 2011 at 9:35 | |||||
| Aug 26, 2011 at 9:35 | vote | accept | herrsimon | ||
| Aug 26, 2011 at 9:35 | |||||
| Aug 25, 2011 at 17:25 | comment | added | Mark | Your question seem to depend strongly on the operator in question. For instance, for "composition operators" (i.e. operators of the form $U_T (f) = f \circ T$, $f \in L^2 (X,\mu)$, $T:X\to X$ "nice"), the pointwise product of two eigenfunctions is also an eigenfunction( as long as it itself lies in $L^2 (X)$) and there are plenty of such operators with discrete spectrum. | |
| Aug 25, 2011 at 3:32 | answer | added | S. Carnahan♦ | timeline score: 3 | |
| Aug 24, 2011 at 18:30 | history | edited | herrsimon | CC BY-SA 3.0 |
Added closeness condition of the Hilbert space under multiplication
|
| Aug 24, 2011 at 18:26 | comment | added | herrsimon | You are right, thanks for commenting on that. Obviously, I was too quick with my generalizing. I added the condition that the Hilbert space should be closed under multiplication. | |
| Aug 24, 2011 at 17:41 | comment | added | BSteinhurst | Some care is necessary, Laplacians on many fractals have domains that aren't algebras so even having the product in the domain again is not something to leave unappreciated. | |
| Aug 24, 2011 at 16:54 | history | edited | herrsimon | CC BY-SA 3.0 |
added 218 characters in body
|
| Aug 24, 2011 at 16:05 | answer | added | paul garrett | timeline score: 7 | |
| Aug 24, 2011 at 15:54 | history | edited | herrsimon |
edited tags
|
|
| Aug 24, 2011 at 14:34 | history | asked | herrsimon | CC BY-SA 3.0 |