Timeline for Singular Sturm-Liouville problems: criterion for discrete spectrum for zero potential ($q=0$) and Hermite Polynomials
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 6, 2020 at 19:32 | vote | accept | stewori | ||
| Apr 6, 2020 at 19:32 | comment | added | stewori | Right :) I had just found the example in Section 5 of your paper 1 which explains the construction. Then I wrote "forget the question about $u$". The example is so hidden at the end... I had overlooked it when I skimmed through the paper at first. | |
| Apr 5, 2020 at 17:17 | comment | added | Christian Remling | @stewori: Yes, that's correct (what you say about the whole line problem). The other solution $u$ does make another appearance, though I don't call it that, the general form of $H$ is $H=w \bigl( \begin{smallmatrix} u^2 & uv \\ uv & v^2 \end{smallmatrix} \bigr)$. | |
| Apr 5, 2020 at 16:29 | comment | added | stewori | Forget the question about $u$, I see, it's just another solution for $\lambda = 0$. Read it too quickly... | |
| Apr 5, 2020 at 14:21 | comment | added | stewori | Wow, that's a stunningly beautiful criterion. Thanks for this work! Do I understand correctly that for the full line, (1) must additionally hold with every $\infty$ replaced by $-\infty$? You defined $u=1$ but did not use it any more. Was it a typo? | |
| Apr 4, 2020 at 19:55 | history | edited | Christian Remling | CC BY-SA 4.0 |
added 17 characters in body
|
| Apr 4, 2020 at 19:48 | history | answered | Christian Remling | CC BY-SA 4.0 |