2024/06/05 by Natalia Zorii, Zorii, Natalia
Mathematics · #31C15 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2406.11874
openalex publication_date 2024/06/05 · openalex created_date 2024/06/20 · openalex updated_date 2026/07/28
For suitable kernels on a locally compact space, we develop a theory of inner (outer) pseudo-balayage of quite general signed Radon measures (not necessarily of finite energy) onto quite general sets (not necessarily closed). Such investigations were initiated in Fuglede's study (Anal. Math., 2016), which was, however, mainly concerned with the outer pseudo-balayage of positive measures of finite energy. The results thereby obtained solve Fuglede's problem, posed to the author in a private correspondence (2016), whether his theory could be extended to measures of infinite energy. An application of this theory to weighted minimum energy problems is also given.