- Tytuł:
- "Counterexamples" to the harmonic Liouville theorem and harmonic functions with zero nontangential limits
- Autorzy:
- Bonilla, A.
- Powiązania:
- https://bibliotekanauki.pl/articles/965789.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
nontangential limits
universal function
approximation
Liouville harmonic theorem
Radon transform
harmonic functions - Opis:
- We prove that, if μ>0, then there exists a linear manifold M of harmonic functions in $ℝ^N$ which is dense in the space of all harmonic functions in $ℝ^N$ and lim_{{‖x‖→∞} {x ∈ S}} ‖x‖^{μ}D^{α}v(x) = 0 for every v ∈ M and multi-index α, where S denotes any hyperplane strip. Moreover, every nonnull function in M is universal. In particular, if μ ≥ N+1, then every function v ∈ M satisfies ∫_H vdλ =0 for every (N-1)-dimensional hyperplane H, where λ denotes the (N-1)-dimensional Lebesgue measure. On the other hand, we prove that there exists a linear manifold M of harmonic functions in the unit ball of $ℝ^N$, which is dense in the space of all harmonic functions and each function in M has zero nontangential limit at every point of the boundary of .
- Źródło:
-
Colloquium Mathematicum; 2000, 83, 2; 155-160
0010-1354 - Pojawia się w:
- Colloquium Mathematicum
- Dostawca treści:
- Biblioteka Nauki
Artykuł