Timeline for A question regarding Hermite polynomials and exponential operators $\exp[e^{x^2/2}p(\frac{d}{dx})e^{-x^2/2}]f(x)$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 18, 2023 at 1:44 | comment | added | Michael Engelhardt | @Mirar - depends on what your small parameters are. You've already written down something like a perturbative expansion for the case that $p$ has small coefficients. It's thinkable to generalize this to the case that only some of the coefficients can be regarded as small. If the other terms correspond to a sufficiently simple, tractable problem, you can resum those and are then left with the perturbative series in the small terms. | |
| Aug 16, 2023 at 13:10 | comment | added | Mirar | What about approximation? | |
| Aug 16, 2023 at 7:00 | comment | added | Michael Engelhardt | I'm somewhat pessimistic. In the case of the Weierstrass transform, the operator is sufficiently simple such that one can identify it with a shift operator (after some manipulations). Once you start to go to more complicated operators, closed-form expressions quickly become unattainable. Maybe for selected polynomials $p$, it's still possible, but a formula for general $p$ ... I don't know. | |
| Aug 16, 2023 at 6:39 | comment | added | Mirar | Similar to en.m.wikipedia.org/wiki/Weierstrass_transform | |
| Aug 16, 2023 at 6:37 | comment | added | Mirar | I would like to get ride of the operator. Not sure this solution helps. | |
| Aug 16, 2023 at 6:29 | history | answered | Michael Engelhardt | CC BY-SA 4.0 |