Modules of solutions of the Helmholtz equation arising from eigenfunctions of the Dirac operator
Marmolejo-Olea, Emilio ; Pérez-Esteva, Salvador ; Shapiro, Michael
Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, p. 175-192 / Harvested from Project Euclid
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We study modules of solutions of the equation $DF=F$, where $F$ is a function in the plane with values in the quaternions and $D$ is the Dirac operator. The functions $F$ will belong to the Sobolev-type space of all functions in $L^{p}(\Omega,|x|^{-3}dx)$ jointly with their angular and radial derivatives, and where $\Omega$ is the complement of the unit disk in $\mathbb{R}^{2}$. The resulting spaces are right Banach modules over the quaternions. When $p=2$ we calculate the reproducing kernel of this space and explain its reproducing properties when $p\neq2$.
Publié le : 2005-04-14
Classification:  Helmholtz equation,  reproducing kernel,  Dirac operator,  46E15,  39G35 
@article{1117805082,
     author = {Marmolejo-Olea, Emilio and P\'erez-Esteva, Salvador and Shapiro, Michael},
     title = {Modules of solutions of the Helmholtz equation arising from eigenfunctions of
the Dirac operator},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {5},
     year = {2005},
     pages = { 175-192},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1117805082}
}

Marmolejo-Olea, Emilio; Pérez-Esteva, Salvador; Shapiro, Michael. Modules of solutions of the Helmholtz equation arising from eigenfunctions of
the Dirac operator. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, pp.  175-192. http://gdmltest.u-ga.fr/item/1117805082/