Timeline for Is the space of rapidly decreasing (non-smooth) functions nuclear?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 29, 2014 at 10:53 | comment | added | Matthias Ludewig | What is the name of that paper by Pietsch? | |
| Feb 20, 2014 at 7:55 | comment | added | Jochen Wengenroth | Another reason for the ubiquity is of course the Komura-Komura theorem saying that every nuclear locally convex space is isomorphic to a subspace of $s^I$ for some index set $I$. A good reference is the book Introduction to Functional Analysis of Meise and Vogt. | |
| Feb 19, 2014 at 17:48 | comment | added | alpha | @Goulifet. Added as an afterthought. Pietsch' method also explains the ubiquity of the space $s$ in the theory of test functions. The spaces introduced in his article are isomorphic to this one whenever the eigenvalues of the differential operator are asymptotically like a (positive) power of $n$ (this is not in the quoted article but is an easy consequence of its methods). Of course, many of the classical partial differential operators of theoretical physics (Laplace and Schrödinger) satisfy this condition. | |
| Feb 19, 2014 at 12:29 | vote | accept | Goulifet | ||
| Feb 19, 2014 at 10:07 | history | edited | alpha | CC BY-SA 3.0 |
added paragraph
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| Feb 19, 2014 at 9:59 | history | answered | alpha | CC BY-SA 3.0 |