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Harmonic Functions on Four Dimensions by Johnston, William; Moore, Sara; Wahl, Rebecca G. is a scholarly article available to read on EtoBox.

What is Harmonic Functions on Four Dimensions about?

This paper develops theory for a newly-defined bicomplex hyperbolic harmonic function with four real-dimensional inputs, in a way that generalizes the connection between real harmonic functions with two real-dimensional inputs and complex analytic functions. For example, every bicomplex hyperbolic harmonic function appears as this paper's newly-defined hyperbolic real part of a bicomplex analytic function, just as every real harmonic function with two real-dimensional inputs is the real part of a complex analytic function. In addition, this connection produces a unique (up to additive constant) and newly-defined hyperbolic harmonic conjugate function, just as every real harmonic function has a unique (up to additive constant) real harmonic conjugate. Finally, the paper determines a bicomplex Poisson kernel function that produces a corresponding integral representation for bicomplex harmonic functions, one that generalizes the complex harmonic function Poisson integral representation.

Author

Johnston, William; Moore, Sara; Wahl, Rebecca G.

Published

2023

Language

EN