On derivatives of spherical monogenics

Abstract

The main objective of this article is to consider complete orthonormal systems of monogenic polynomials together with their hypercomplex derivatives. Desired is that the derivatives of the basis polynomials are again basis functions from the original system. Based on this result, we prove an orthogonal decomposition of the space of square integrable monogenic functions with respect to the derivatives of arbitrary order.

§Dedicated to Professor Guochun Wen on the occasion of his 75th birthday.

Keywords:

• Spherical monogenics
• Hypercomplex derivative
• Series expansions

Keywords:

• AMS Subject Classifications: 30G35
• 41A10
• 33C55

Notes

§Dedicated to Professor Guochun Wen on the occasion of his 75th birthday.