Abstract
In this chapter we investigate more closely the relation between a positive harmonic function V(ζ) in the upper half-plane and the measure µ occuring in its canonical representation. It is clear that the function is perfectly smooth, indeed harmonic, near any real point λ0 which is at a positive distance from the support of the measure. There is also no loss of generality in our supposing that we study the function near the origin, that α =0 and that the measure is supported by the interval [−1,1].
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© 1974 Springer-Verlag Berlin Heidelberg
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Donoghue, W.F. (1974). Fatou Theorems. In: Monotone Matrix Functions and Analytic Continuation. Die Grundlehren der mathematischen Wissenschaften, vol 207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65755-9_4
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DOI: https://doi.org/10.1007/978-3-642-65755-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65757-3
Online ISBN: 978-3-642-65755-9
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