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On the role of arbitrary order Bessel functions in higher dimensional Dirac type equations

Authors:	Isabel Cação Denis Constales Rolf Sören Krausshar

Institution:	(1) Departamento de Matemática, Universidade de Aveiro, Campus Universitário Santiago, P-3810-193 Aveiro, Portugal;(2) Department of Mathematical Analysis, Ghent University, Building S-22, Galglaan 2, B-9000 Ghent, Belgium

Abstract:	This paper exhibits an interesting relationship between arbitrary order Bessel functions and Dirac type equations. Let $D: = {\sum\limits_{i = 1}^n {\frac{\partial }{{\partial x_{i} }}e_{i}}}$ be the Euclidean Dirac operator in the n-dimensional flat space $\mathbb{R}^{n},{\mathbf{E}}: = {\sum\limits_{i = 1}^n {x_{i} \frac{\partial }{{\partial x_{i} }}}}$ the radial symmetric Euler operator and α and λ be arbitrary non-zero complex parameters. The goal of this paper is to describe explicitly the structure of the solutions to the PDE system $\left {D - \lambda - (1 + \alpha )\frac{{\text{x}}} {{\text{\|x\|}}^{2}}{\mathbf{E}}} \right]f = 0$ in terms of arbitrary complex order Bessel functions and homogeneous monogenic polynomials. Received: 27 October 2005

Keywords:	30G35 33C10
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