Reduced-quaternion inframonogenic functions on the ball

Resumen

A function from a domain in to the quaternions is said to be inframonogenic if
, where
. All inframonogenic functions are biharmonic. In the context of functions taking values in the reduced quaternions, we show that the inframonogenic homogeneous polynomials of degree form a subspace of dimension . We use the homogeneous polynomials to construct an explicit, computable orthogonal basis for the Hilbert space of square-integrable inframonogenic functions defined in the ball in .

Autores

• C. Álvarez-Peña
• J. Morais
• R. Michael Porter

Revista Math. Meth. Appl. Sci.

https://doi.org/10.1002/mma.9600