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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.20571 |
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Table of Contents:
- We investigate the explicit expression for the principal eigenvalue $λ_{1}^{X}(D)$ for a large class of compound Poisson processes $X$ on a bounded open set $D$ by examining its spectral heat content. When the jump density of the compound Poisson process is radially symmetric and strictly decreasing, we demonstrate that balls are the unique minimizers for $λ_{1}^{X}(D)$ among all sets with equal Lebesgue measure. Furthermore, we show that this uniqueness fails if the jump density is not strictly decreasing.