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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/2405.05265 |
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Table of Contents:
- For operators $A$, it is sometimes possible to define $e^{At}$ as an operator in and of itself provided it meets certain regularity conditions. Like $e^{λx}$ for ODEs, this operator is useful for solving PDEs involving the operator $A$. We call the set of $e^{At}$ a semigroup generated by $A$. In this paper, we discuss the properties of semigroups generated by the fractional integral, an operator appearing in PDEs in increasingly many fields, over Bochner-Lebesgue spaces.