Timeline for product of two generalized functions
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 1, 2021 at 18:44 | comment | added | Didine Zaidni | Let u and v be distributions in D′(U). Assume that there is no point (x, k) in WF(u) such that (x, −k) belongs to WF(v), then the product uv can be defined. (Lars Hörmander) | |
| Dec 1, 2021 at 14:33 | comment | added | hordubal | It depends on how you define the product, i.e., under which conditions on the distributions. In my book, it is well-defined but if this bothers you, you can smooth them out to very good $C^\infty$ approximations by the usual methods. | |
| Dec 1, 2021 at 12:42 | comment | added | Didine Zaidni | Thank you @bathalf15320 , but I am not sur if the product r_n^2 is well defined in the sens of generalized functions, for exemple the Heaviside function verifies that H.H = H but the product H.H is not well defined becuse does not satisfy the leibniz rule. | |
| Dec 1, 2021 at 8:44 | comment | added | bathalf15320 | The standard example for this kind of question is the sequence of Rademacher functions--converge to zero in various weak topoloy but the squares converge to $1$. | |
| Nov 30, 2021 at 18:22 | history | edited | Didine Zaidni | CC BY-SA 4.0 |
edited body
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| S Nov 30, 2021 at 17:27 | review | First questions | |||
| Nov 30, 2021 at 17:35 | |||||
| S Nov 30, 2021 at 17:27 | history | asked | Didine Zaidni | CC BY-SA 4.0 |