Pointwise convergence and radial limits of harmonic functions. (English) Zbl 1082.31001
Following the work of J. Lukeš, J. Malý, I. Netuka, M. Smrcka and J. Spurný [Isr. J. Math. 134, 255–287 (2003; Zbl 1031.35011)], the authors characterize the real-valued functions on a compact set \(K\) in \(\mathbb{R}^n\) that can be expressed as the pointwise limit of a sequence of functions each of which are harmonic on some neighborhood of \(K\). They also characterize the functions on the unit sphere which are the radial limits of entire harmonic functions.
Reviewer: Yusuf Avci (Ýstanbul)
MSC:
| 31B05 | Harmonic, subharmonic, superharmonic functions in higher dimensions |
| 31B20 | Boundary value and inverse problems for harmonic functions in higher dimensions |
Keywords:
probability measure; Baire-one function; Baire category; coarsest topology; fine harmonicityCitations:
Zbl 1031.35011References:
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