2024/07/18 by Natalia Zorii, Zorii, Natalia
Engineering · #31C15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Simulation and Modeling Applications
paper · pdf · doi:10.48550/arxiv.2407.13440
openalex publication_date 2024/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the theory of inner and outer balayage of positive Radon measures on a locally compact space X to arbitrary A⊂ X with respect to suitable, quite general function kernels, developed in a series of the author's recent papers, we find conditions ensuring the validity of the integral representations. The results thereby obtained do hold and seem to be largely new even for several interesting kernels in classical and modern potential theory, which looks promising for possible applications. As an example of such applications, we analyze how the total mass of a measure varies under its balayage with respect to fractional Green kernels.