Timeline for Does the functional square root of the cosine admit a vector-based interpretation?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 3, 2020 at 18:23 | comment | added | Gottfried Helms | Hmm, for me the idea of iteration of a function means, that the input and the output have the same structure. So they both may be a scalar, maybe a two-component vector or $2 \times 2$-matrix (for instance for $2$-D rotation matrices) , or infinite vectors of coefficients (for instance in the context of Carleman-matrices, which give a "vandermonde-vector" as input as well as output - here I use "vand. vector" meaning an infinite vector of an argument $x$ as $V(x) = [1,x,x^2,x^3,...]$). Could we define some structure first which is stable between input & output for your problem? | |
| S Sep 22, 2020 at 23:04 | history | bounty ended | CommunityBot | ||
| S Sep 22, 2020 at 23:04 | history | notice removed | CommunityBot | ||
| Sep 15, 2020 at 22:27 | comment | added | Piotr Hajlasz | I am removing my vote to close. | |
| S Sep 14, 2020 at 21:56 | history | bounty started | Max Lonysa Muller | ||
| S Sep 14, 2020 at 21:56 | history | notice added | Max Lonysa Muller | Draw attention | |
| Sep 13, 2020 at 16:14 | comment | added | Max Lonysa Muller | ... It therefore lends itself well to be interpreted from a geometric and linear-algebraic perspective. Such a perspective may be lacking in the current literature on functional equations | |
| Sep 13, 2020 at 16:10 | comment | added | Max Lonysa Muller | @PiotrHajlasz I think this question is interesting because it may cast a renewed understanding of the functional square root of the cosine. It seems to me most effort to find this root has so far been directed at finding its Taylor series coefficients. While progress has been made in this direction, it has so far not enabled us to retrieve a closed-form analytic expression for the root. In contrast to many other functions, the cosine of two vectors has an elegant and simple representation in vectorial terms... (cont'd) | |
| Sep 12, 2020 at 13:26 | review | Close votes | |||
| Sep 14, 2020 at 22:07 | |||||
| Sep 12, 2020 at 13:11 | comment | added | Max Lonysa Muller | Could the person(s) who voted down and/or to close please explain his/her motivations? | |
| Sep 12, 2020 at 11:16 | history | asked | Max Lonysa Muller | CC BY-SA 4.0 |