Abstract
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 (u, ξ, δ), A(u, ξ, δ), and αu can play the same role when N = 1 as when N > 1, but more direct methods are sometimes clearer.
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© 1984 Springer-Verlag New York Inc.
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Doob, J.L. (1984). One-Dimensional Potential Theory. In: Classical Potential Theory and Its Probabilistic Counterpart. Grundlehren der mathematischen Wissenschaften, vol 262. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5208-5_14
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DOI: https://doi.org/10.1007/978-1-4612-5208-5_14
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-9738-3
Online ISBN: 978-1-4612-5208-5
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