FRACTIONAL-LINEAR FUNCTIONS OF h-COMPLEX ARGUMENT
Author consider having ⅅ- derivative and ⅅ-differentiable mappings f:A → ⅅ, A ⊂ ⅅ, where is the set of all h-complex numbers, i.e. numbers shape x+jy, where ,x,y ∈ R, j2=1, j≠±1. Such mappings are called h-analytic functions. Theirs real and imaginary parts satisfy the string oscillation equation. The general expression for h-analytic functions is known. One of the properties of such functions: images of characteristics x+y=const are characteristics u+v=const. Symmetry with respect to hyperbolas is introduced and the property of preservation of symmetric pairs of points under fractional- linear mappings is established.