Contragenic Functions of Three Variables
Complex Variables
2024-10-15 v1
Abstract
It is shown that harmonic functions from a simply connected domain in R^3 to R^3 cannot always be expressed as a sum of a monogenic (hyperholomorphic) function and an antimonogenic function, in contrast to the situation for complex numbers or quaternions. Harmonic functions orthogonal in L_2 to all such sums are termed "contragenic" and their properties are studied. A "Bergman kernel" and is derived, whose corresponding operator vanishes precisely on the contragenic functions. A graded orthonormal basis for the contragenic function in the ball B^3 is given.
Cite
@article{arxiv.1207.1730,
title = {Contragenic Functions of Three Variables},
author = {Cynthia Alvarez-Peña and R. Michael Porter},
journal= {arXiv preprint arXiv:1207.1730},
year = {2024}
}
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