Volume estimates of sublevel sets of real polynomials

2017/11/13 by Dieu, Nguyen Quang, Hung, Dau Hoang, Pham, Tien Son +1 · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.04544

Abstract

We give upper bounds for volume of sublevel sets of real polynomials. Our method is to combine a version of global Lojasiewicz inequality with some well known estimate on volume of tubes around real algebraic sets. Some applications to oscillatory integrals and integration indices of real polynomial are also given.

Cited by

• The Multivariate Herglotz-Nevanlinna Class: Superresolution

Related

• Bounds for volumes of sub-level sets of polynomials and applications
• Hausdorff approximations and volume of tubes of singular algebraic sets
• Local dimension-free estimates for volumes of sublevel sets of analytic functions
• Density of real and complex decomposable univariate polynomials
• Volume Of Sub-level Sets Of Homogeneous Polynomials