On conjugate harmonic pairs $(U_r, V_{r-1})$ of multi-vector valued functions

Delanghe, Richard

Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, p. 483-491 / Harvested from Project Euclid

Résumé

Let $\mathbb{R}_{0,m}$ be the real Clifford algebra constructed over the real quadratic space $\mathbb{R}^{0,m}$ with signature $(0,m)$ and let $U_r$ be an $\mathbb{R}^+_{0,m}$-valued harmonic function in an appropriate open domain $\Omega$ of $\mathbb{R}^{m+1}$ $(0 < r \leq m; m \geq 2)$. Then a necessary and sufficient condition is given upon $U_r$ for the existence of an $\mathbb{R}^{r-1}_{0,m}$-valued harmonic function in $\Omega$ which is conjugate to $U_r$.

Publié le : 2007-09-14
Classification: Clifford analysis, multi-vector valued functions, conjugate harmonic pairs, 30G35

@article{1190994209,
     author = {Delanghe, Richard},
     title = {On conjugate harmonic pairs $(U\_r, V\_{r-1})$ of multi-vector valued functions},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {13},
     number = {5},
     year = {2007},
     pages = { 483-491},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1190994209}
}

Delanghe, Richard. On conjugate harmonic pairs $(U_r, V_{r-1})$ of multi-vector valued functions. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp.  483-491. http://gdmltest.u-ga.fr/item/1190994209/