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Riesz capacity: monotonicity, continuity, diameter and volume
- Publication Year :
- 2024
-
Abstract
- Properties of Riesz capacity are developed with respect to the kernel exponent $p \in (-\infty,n)$, namely that capacity is monotonic as a function of $p$, that its endpoint limits recover the diameter and volume of the set, and that capacity is left-continuous with respect to $p$ and is right-continuous provided (when $p \geq 0$) that an additional hypothesis holds. Left and right continuity properties of the equilibrium measure are obtained too.
- Subjects :
- Mathematics - Classical Analysis and ODEs
31A15, 31B15
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2406.10781
- Document Type :
- Working Paper