Timeline for Identification of Fock space and the $L^2$ space of tempered distributions
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 8 at 17:07 | comment | added | CBBAM | @AbdelmalekAbdesselam After doing some more reading on Weiner chaos the general construction is clear, but how does it ensure that the spaces $\mathcal{F}_n$ are symmetric? Also, is the Weiner chaos the same thing as Fock space but with a different name in the probability literature or is there a more subtle connection between the two? | |
| Aug 8 at 15:24 | comment | added | CBBAM | @AbdelmalekAbdesselam Thank you. Weiner chaos is new to me but seems to be exactly what I am looking for! | |
| Aug 8 at 14:54 | comment | added | Abdelmalek Abdesselam | First you define $\mathcal{G}_n$ as the space of polynomials in $\phi$ of degree at most $n$. Namely this is the linear span of functions $\phi\mapsto \phi(f_1)\cdots\phi(f_k)$ with $k\le n$. Then you do a kind of Gram-Schmidt orthogonalization, and define $\mathcal{F}_n$ as the orthogonal complement of $\mathcal{G}_{n-1}$ inside $\mathcal{G}_n$. If GJ is not clear, you can look this up in the probability literature. You will need to switch terminology to "Wiener chaos" instead of "Fock space". Standard refs are books by Svante Janson and David Nualart. | |
| Aug 8 at 10:46 | comment | added | no upstairs | Fock........... | |
| Aug 8 at 9:22 | history | edited | gmvh | CC BY-SA 4.0 |
Changed dimension to $d$ to avoid confusion with particle number $n$ subsequently introduced
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| Aug 8 at 3:39 | history | asked | CBBAM | CC BY-SA 4.0 |