Timeline for (Real) algebraic geometry for (real) trigonometric polynomials?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 3, 2011 at 20:54 | answer | added | Thierry Zell | timeline score: 2 | |
| Jun 3, 2011 at 19:50 | comment | added | Helge | So one issue that puzzles me: Is there an analog of Bezout's theorem. So given 2 trigonometric polynomials $f$ and $g$ in two variables that don't have a common irreducible factor (as trigonometric polynomials). Is it true that the number of solutions of $f(x) = g(x) = 0$ is bounded by $4 \mathrm{deg}(f) \mathrm{deg}(g)$? ......... Also it would be interesting to see carefully stated versions of the claims about dimensions. | |
| Jun 3, 2011 at 18:50 | comment | added | Thierry Zell | The answer is a definite yes, there is extensive literature addressing these. But it is somewhat scattered and I don't know that it represents a "field" per se, so it's hard to give precise pointers unless you have a specific question in mind. E.g. I've seen the $(C_j, S_j)$ technique you mention used in Engineering problems, Khovanskii has results about number of solutions... There's lots more that escapes me right now. | |
| Jun 3, 2011 at 18:10 | history | asked | Helge | CC BY-SA 3.0 |