DOI: 10.1063/5.0149554 ISSN: 0022-2488

Almansi decomposition of polynomials of quaternionic Dirac operators

Guangbin Ren, Lizheng Zhang
  • Mathematical Physics
  • Statistical and Nonlinear Physics

This article presents an innovative extension of the classical Almansi decomposition. Traditionally, the Almansi decomposition is employed to decompose polymonogenic functions into their monogenic counterparts, thereby elucidating the relationship between the Dirac operator and its successive iterations. Diverging from this conventional method, the new extension delves into the kernel of a polynomial related to the quaternionic Dirac operator, as opposed to focusing on the iterated operator. This is achieved by employing a polynomial-based partition of unity. The outcome of this approach is a distinctive decomposition that leverages the kernel of the Dirac–Helmholtz operators.

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