Timeline for About eigen-functions of the Gaussian kernel
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Sep 22 at 7:02 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
moved image to MO repository (the answer was reactivated on the front page anyway)
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| Nov 28, 2023 at 0:01 | comment | added | QnA | Thanks! I just checked, and the eigenfunction expansion matches the Gaussian kernel well locally around x=z=0, but then they go to zero pretty fast before I can come up with enough higher order Hermite terms. Sort of like Taylor expansion, locally matches very well, but requires much more terms for it to work further out. | |
| Nov 27, 2023 at 11:34 | comment | added | Carlo Beenakker | you can check numerically that sum over $n$ gives 1 for $x=z$; each term is small, but there are infinitely many terms... | |
| Nov 27, 2023 at 4:50 | comment | added | QnA | stupid question, in (11), in 1D case, when x=z goes to infinity, left side of the equation remains one, but from (12) and (13), it looks like all eigenfunctions go to zero due to the exponential term? i.e., the 'diagonal' of the kernel should be the same value, regardless how large the x&z goes, but the eigenfunctions seem to diminish when x&z goes large, how come? | |
| Mar 7, 2019 at 7:35 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
http --> https
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| Apr 23, 2016 at 2:25 | vote | accept | gradstudent | ||
| Apr 22, 2016 at 17:24 | history | answered | Carlo Beenakker | CC BY-SA 3.0 |