Timeline for Nice applications for Schwartz distributions
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 23, 2017 at 10:32 | comment | added | Abdelmalek Abdesselam | Just an update: I actually had a student do a presentation to the rest of the class about this using the more constructive recent proofs by Ortner and Wagner which I think should be better known. | |
| Jan 18, 2017 at 14:42 | comment | added | Pedro Lauridsen Ribeiro | The functional identities for theta functions coming from the Poisson summation formula are precisely the ones used in obtaining KW duality. | |
| Jan 18, 2017 at 10:51 | comment | added | Piero D'Ancona | I know there is a connection with theta functions and modular forms, but my knowledge is limited to the immediate application to functional identities for the theta functions. This is included e.g. in the Wikipedia article on Poisson summation formula | |
| Jan 18, 2017 at 2:01 | comment | added | Pedro Lauridsen Ribeiro | A nice physical application of the Poisson summation formula is Kramers-Wannier duality in statistical mechanics, as done in Kadanoff's book on the subject. | |
| Jan 18, 2017 at 0:37 | comment | added | Abdelmalek Abdesselam | BTW which deeper theories do you have in mind in relation to Poisson summation? I can think of functional equations for the zeta functions but if you have other things in that vein I would be interested in that too. | |
| Jan 18, 2017 at 0:23 | comment | added | Abdelmalek Abdesselam | Thanks! I thought about the ME Thm in relation topic 5 that I mentioned but thank you for pointing out Taylor's treatment of this result. I'll have a look. | |
| Jan 17, 2017 at 23:27 | comment | added | Piero D'Ancona | A simpler result is Poisson's summation formula, which however can be a pointer to much deeper theories. I guess it is not necessary to give a reference for this one. | |
| Jan 17, 2017 at 23:25 | history | answered | Piero D'Ancona | CC BY-SA 3.0 |