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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2206.08820 |
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Table of Contents:
- We study the generator $G$ of the one-dimensional damped wave equation with unbounded damping. We show that the norm of the corresponding resolvent operator, $\| (G - λ)^{-1} \|$, is approximately constant as $|λ| \to +\infty$ on vertical strips of bounded width contained in the closure of the left-hand side complex semi-plane, $\overline{\mathbb{C}}_{-} := \{λ\in \mathbb{C}: \operatorname{Re} λ\le 0\}$. Our proof rests on a precise asymptotic analysis of the norm of the inverse of $T(λ)$, the quadratic operator associated with $G$.