| | |
| | |
Stat |
Members: 3643 Articles: 2'487'895 Articles rated: 2609
28 March 2024 |
|
| | | |
|
Article overview
| |
|
Multiplicity and degree relative to a set | Vincent Grandjean
; Maria Michalska
; | Date: |
11 Oct 2019 | Abstract: | The multiplicity (resp. degree) of a function $f$ relative to a semianalytic
subset $S$ of $mathbb{R}^n$ is the greatest (resp. smallest) exponent among
numbers $j$ such that the inequality $|f(x)|leq C|x|^j$ holds on $S$ near
$0$ (resp. near infinity) for some constant $C$. We show that there exists a
family of curves ${Gamma_d}_{din mathbb{N}}$, determined only by the set,
such that the relative multiplicity of any polynomial of degree $d$ is equal to
its relative multiplicity with respect to $Gamma_d$. Moreover, a semianalytic
family $(S_t)_{tinmathbb{R}^m}$ of sets given by inequalities $f_i+t_ig_igeq
0$ for $i=1,dots, m$ admits a stratification of the parameter space
$mathbb{R}^m$ such that on each component of the top-dimensional stratum the
relative multiplicity function on $mathcal{O}_n$ does not change. Analogous
results, assuming the data are algebraic, hold in the relative degree case. | Source: | arXiv, 1910.5203 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |