Some remarks concerning harmonic functions on homogeneous graphs
2003 ◽
Vol DMTCS Proceedings vol. AC,...
(Proceedings)
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Keyword(s):
International audience We obtain a new result concerning harmonic functions on infinite Cayley graphs $X$: either every nonconstant harmonic function has infinite radial variation in a certain uniform sense, or there is a nontrivial boundary with hyperbolic properties at infinity of $X$. In the latter case, relying on a theorem of Woess, it follows that the Dirichlet problem is solvable with respect to this boundary. Certain relations to group cohomology are also discussed.
The Dirichlet Problem for the Slab with Entire Data and a Difference Equation for Harmonic Functions
2017 ◽
Vol 60
(1)
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pp. 146-153
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Keyword(s):
Keyword(s):
1948 ◽
Vol 44
(2)
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pp. 289-291
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Keyword(s):
Optimal growth of harmonic functions frequently hypercyclic for the partial differentiation operator
2019 ◽
Vol 149
(6)
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pp. 1577-1594
1997 ◽
Vol 49
(1)
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pp. 55-73
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1949 ◽
Vol 45
(2)
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pp. 207-212
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