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June 2005 Modules of solutions of the Helmholtz equation arising from eigenfunctions of the Dirac operator
Emilio Marmolejo-Olea, Salvador Pérez-Esteva, Michael Shapiro
Bull. Belg. Math. Soc. Simon Stevin 12(2): 175-192 (June 2005). DOI: 10.36045/bbms/1117805082

Abstract

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 $p\neq2$.

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Emilio Marmolejo-Olea. Salvador Pérez-Esteva. Michael Shapiro. "Modules of solutions of the Helmholtz equation arising from eigenfunctions of the Dirac operator." Bull. Belg. Math. Soc. Simon Stevin 12 (2) 175 - 192, June 2005. https://doi.org/10.36045/bbms/1117805082

Information

Published: June 2005
First available in Project Euclid: 3 June 2005

zbMATH: 1119.35072
MathSciNet: MR2179962
Digital Object Identifier: 10.36045/bbms/1117805082

Subjects:
Primary: 39G35, ‎46E15

Rights: Copyright © 2005 The Belgian Mathematical Society

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Vol.12 • No. 2 • June 2005
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