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arXiv · 2504.10946

Maximum principles and spectral analysis for the superposition of operators of fractional order

Serena Dipierro·Edoardo Proietti Lippi·Caterina Sportelli·Enrico Valdinoci
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Abstract

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 $-\Delta + (-\Delta)^s$, 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].

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Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli, Enrico Valdinoci. 2025-04-15. Maximum principles and spectral analysis for the superposition of operators of fractional order. https://doi.org/10.1007/s44007-026-00204-1

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