Maximum principles and spectral analysis for the superposition of operators of fractional order
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913030422396928 |
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| author | Dipierro, Serena Lippi, Edoardo Proietti Sportelli, Caterina Valdinoci, Enrico |
| author_facet | Dipierro, Serena Lippi, Edoardo Proietti Sportelli, Caterina Valdinoci, Enrico |
| contents | We consider a "superposition operator" obtained through the continuous superposition of operators of mixed fractional order, modulated by a signed Borel finite measure defined over the set $[0, 1]$. The relevance of this operator is rooted in the fact that it incorporates special and significant cases of interest, like the mixed operator $-Δ+ (-Δ)^s$, the (possibly) infinite sum of fractional Laplacians and allows to consider operators carrying a "wrong sign".
We first outline weak and strong maximum principles for this type of operators. Then, we complete the spectral analysis for the related Dirichlet eigenvalue problem started in [DPLSV25b]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10946 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum principles and spectral analysis for the superposition of operators of fractional order Dipierro, Serena Lippi, Edoardo Proietti Sportelli, Caterina Valdinoci, Enrico Analysis of PDEs We consider a "superposition operator" obtained through the continuous superposition of operators of mixed fractional order, modulated by a signed Borel finite measure defined over the set $[0, 1]$. The relevance of this operator is rooted in the fact that it incorporates special and significant cases of interest, like the mixed operator $-Δ+ (-Δ)^s$, the (possibly) infinite sum of fractional Laplacians and allows to consider operators carrying a "wrong sign". We first outline weak and strong maximum principles for this type of operators. Then, we complete the spectral analysis for the related Dirichlet eigenvalue problem started in [DPLSV25b]. |
| title | Maximum principles and spectral analysis for the superposition of operators of fractional order |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.10946 |