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Approximation by Continuous Potentials

In: Potential Theory

Author

Listed:
  • Jürgen Bliedtner

    (Universität Frankfurt, Fachbereich Mathematik)

  • Wolfhard Hansen

    (Universität Bielefeld, Fakultät für Mathematik)

Abstract

In this note we improve theorems in [1] and [2] dealing with approximation of (super)harmonic functions by continuous potentials. That is, we intend to show that for every finely open set G of a balayage space (X, W) there exists a continuous potential q ε P such that $$S(G) = \overline {P + \mathbb{R}q} ,H(G) = \overline {H(q)}$$ .

Suggested Citation

  • Jürgen Bliedtner & Wolfhard Hansen, 1988. "Approximation by Continuous Potentials," Springer Books, in: Josef Král & Jaroslav Lukeš & Ivan Netuka & Jiří Veselý (ed.), Potential Theory, pages 53-58, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0981-9_7
    DOI: 10.1007/978-1-4613-0981-9_7
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