Timeline for How far can one get by counting spaces of solutions this way?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 27, 2023 at 8:43 | comment | added | Thomas Rot | Sometimes you can write down a fredholm map, whose index measures morally the relative dimensions of two spaces. | |
| Aug 27, 2023 at 7:50 | comment | added | Malkoun | @user378654, this is interesting, your comment about people working in inverse problems. I am not familiar with that area, but I can see how trying to guess a dimension heuristically can be helpful as a preliminary step. | |
| Aug 27, 2023 at 2:58 | comment | added | user378654 | I guess a different direction would be like Lyapunov-Schmidt reduction and implicit function theorem arguments to rigorously "mod out" by obvious invariances in a nonlinear context. But that doesn't sound quite like what you have in mind. | |
| Aug 27, 2023 at 2:56 | comment | added | user378654 | I have seen people working in inverse problems do these kinds of variable-counting heuristics. They are trying to understand questions like: I give you a bunch of solutions to my PDE, now you guess what my PDE was. This similarly has some a priori ambiguity about how much data is needed vs. how much freedom I have in my selection of PDE (maybe I am free to choose some but not all the coefficients, and I give you some but not all information about the solutions, etc). I don't work in this area myself, so can't give a more serious answer. | |
| Aug 26, 2023 at 20:46 | history | asked | Malkoun | CC BY-SA 4.0 |