# On a Runge theorem over $${\mathbb {R}}_3$$

@article{Bisi2021OnAR,
title={On a Runge theorem over \$\$\{\mathbb \{R\}\}\_3\$\$},
author={Cinzia Bisi and Antonino De Martino and Joerg Winkelmann},
journal={Annali di Matematica Pura ed Applicata (1923 -)},
year={2021}
}
• Published 14 September 2021
• Mathematics
• Annali di Matematica Pura ed Applicata (1923 -)
In this paper we investigate a topological characterization of the Runge theorem in the Clifford algebra R3 via the description of the homology groups of axially symmetric open subsets of the quadratic cone in R3.

## References

SHOWING 1-10 OF 46 REFERENCES

• Mathematics
• 2011
In this paper we introduce and study rational slice monogenic functions. After proving a decomposition theorem for such functions, we are able to prove the Runge approximation theorem for slice
• Mathematics
The Journal of Geometric Analysis
• 2018
We investigate slice-quaternionic Hopf surfaces. In particular, we construct new structures of slice-quaternionic manifold on $${\mathbb {S}}^1\times {\mathbb {S}}^7$$S1×S7, we study their group of
• Mathematics
• 2018
In this paper we survey the theory of holomorphic approximation, from the classical nineteenth century results of Runge and Weierstrass, continuing with the twentieth century work of Oka and Weil,
• Mathematics
• 2014
We study two types of series over a real alternative $^*$-algebra $A$. The first type are series of the form $\sum_{n} (x-y)^{\punto n}a_n$, where $a_n$ and $y$ belong to $A$ and $(x-y)^{\punto n}$
• Mathematics
• 2002
In this article some generalizations to eight dimensional real algebras of the notion of Cauchy-Fueter regularity are introduced, by defining suitable operators. Some properties of the nullsolutions
• Mathematics
Annales Academiae Scientiarum Fennicae Mathematica
• 2019
Given a complex meromorphic function, it is well defined its Riesz measure in terms of the laplacian of the logarithm of its modulus. Moreover, related to this tool, it is possible to prove the
• Mathematics
Indiana University Mathematics Journal
• 2022
In this paper we investigate the Brolin's theorem over $\mathbb{H}$, the skew field of quaternions. Moreover, considering a quaternionic polynomial $p$ with real coefficients, we focus on the