Timeline for To which space does the derivative of a function in Fock space belong?
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9 events
| when toggle format | what | by | license | comment | |
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| Mar 27, 2023 at 8:59 | comment | added | terceira | There is a useful rule of thumb that differentiation "never" acts on an infinite dimensional Banach space (this can be formalised in various ways). One of many reasons why lcs's raise their ugly heads in functional analytic approaches to o.d.e.'s and p.d.e.'s. | |
| Mar 26, 2023 at 22:14 | history | became hot network question | |||
| Mar 26, 2023 at 17:14 | vote | accept | user975628 | ||
| Mar 26, 2023 at 13:51 | history | edited | Michael Engelhardt | CC BY-SA 4.0 |
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| Mar 26, 2023 at 13:40 | answer | added | Alexandre Eremenko | timeline score: 4 | |
| Mar 26, 2023 at 13:37 | comment | added | Yemon Choi | I think so, but I have not done the calculation. You can write down the $F^2_\alpha$ norm of $f$ in terms of its Taylor coefficients (just rewrite $dA(z)$ in polar co-ordinates and use known formulas for moments of the Gaussian) | |
| Mar 26, 2023 at 13:13 | comment | added | user975628 | Thank you! Could be choose an arbitrary $\beta > \alpha$ instead? | |
| Mar 26, 2023 at 13:03 | comment | added | Yemon Choi | I think the answer to your last question is no. If we could take $\beta=\alpha$ then differentiation would be a linear map $D$ from the Hilbert space $F^2_\alpha$ to itself. Then I think one can use the Closed Graph Theorem (for linear maps between Banach spaces) to show that $D$ is continuous with respect to the HSp norm, hence $D$ would have to be a bounded linear map wit hrespect to the HSp norm, but this is easily contradicted by considering $D(z^n)$ for larger and larger $n$. | |
| Mar 26, 2023 at 12:50 | history | asked | user975628 | CC BY-SA 4.0 |