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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1912.10511 |
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Table of Contents:
- Using a version of Hironaka's resolution of singularities for real-analytic functions, any elliptic multiplier $\mathrm{Op}(p)$ of order $d>0$, real-analytic near $p^{-1}(0)$, has a fundamental solution $μ_0$. We give an integral representation of $μ_0$ in terms of the resolutions supplied by Hironaka's theorem. This $μ_0$ is weakly approximated in $H^t_{\mathrm{loc}}(\mathbb{R}^n)$ for $t<d-\frac{n}{2}$ by a sequence from a Paley-Wiener space. In special cases of global symmetry, the obtained integral representation can be made fully explicit, and we use this to compute fundamental solutions for two non-polynomial symbols.