On the pointwise converse of Fatou's theorem for Euclidean and real hyperbolic spaces (Q2089810)
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scientific article; zbMATH DE number 7606047
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the pointwise converse of Fatou's theorem for Euclidean and real hyperbolic spaces |
scientific article; zbMATH DE number 7606047 |
Statements
On the pointwise converse of Fatou's theorem for Euclidean and real hyperbolic spaces (English)
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24 October 2022
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This article provides an extension of a result of L. Loomis and W. Rudin, regarding boundary behavior of positive harmonic functions on the upper half space \(\mathbb{R}^{n+1}_+\). This new result is next used to investigate the boundary behavior of certain nonnegative eigenfunctions of the Laplace-Beltrami operator on real hyperbolic space \(\mathbb{H}_n\) as well as to investigate the large time behavior of solutions of the heat equation.
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Fatou theorem
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Euclidean space
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hyperbolic space
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0.8849288
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0.8733274
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0.86269176
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0.8591781
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