Balayage spaces on topological sums. (English) Zbl 0691.31004

Potential theory, Proc. Conf., Prague/Czech. 1987, 237-246 (1988).
[For the entire collection see Zbl 0675.00009.]
Using the terminology and notations of axiomatic potential theory as developed by J. Bliedtner and W. Hansen [Potential theory (1986)], and others, this paper deals
1\(\circ \) with the determination of a balayage space \((E_ 1+E_ 2,W)\) on a topological sum by means of subspaces \((E_ 1,W_ 1),(E_ 2,W_ 2)\) and associated transition kernels \(R_ 1,R_ 2\) and, conversely,
2\(\circ \) with given \((E_ 1,W_ 1),(E_ 2,W_ 2)\) and appropriate kernels \(R_ 1,R_ 2\), to find NASC for the existence of a unique balayage space \((E_ 1+E_ 2,W)\) characterized by the data and having \((E_ 1,W_ 1),(E_ 2,W_ 2)\) as subspaces and \(R_ 1,R_ 2\) as transition kernels.
Reviewer: E.J.Akutowicz


31D05 Axiomatic potential theory


Zbl 0675.00009