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Erschienen in:
2001 | OriginalPaper | Buchkapitel
One-Dimensional Potential Theory
verfasst von : Joseph L. Doob
Erschienen in: Classical Potential Theory and Its Probabilistic Counterpart
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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The one-dimensional version of classical potential theory is so special that its discussion has been deferred to this chapter, and much of this theory is so elementary that it will be left to the reader to formulate and justify. A ball in ℝ with center ξ is an open interval with midpoint ξ, and the averages L(u, ξ, δ), and Aαu can play the same role when N=1 as when N>1, but more direct methods are sometimes clearer.