Timeline for On the regularity of certain continuous algebraic functions
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jun 9, 2021 at 9:19 | comment | added | Peter O. | I believe I understand: any algebraic function over rationals can be rewritten as a convergent Puiseux series, and is thus Hölder continuous since the series has only additions, multiplications, and radicals; and polynomially bounded by choosing $n$ large enough. | |
| Jun 9, 2021 at 8:28 | comment | added | Dmitri Panov | Peter, it might be that I don't understand your question. I consider the case of real numbers, i.e. when $P(x,y)$ is a polynomial on $\mathbb R^2$ with real (or if you want rational) coefficients. The only thing that I say is that a converging power series $\sum_{i=1}^\infty a_i x^{i/k}$ is Holder (here $k>0$ is integer). Do you agree with this? | |
| Jun 9, 2021 at 7:49 | comment | added | Peter O. | I don't see how the two claims follow from the convergence of Puiseux series, especially when the polynomial's coefficients must be rational numbers (and not, say, numbers in an algebraically closed field such as the complex numbers). You should edit your answer to give more detail on your proof. | |
| Jun 8, 2021 at 22:12 | history | answered | Dmitri Panov | CC BY-SA 4.0 |