I've found quite a number of articles on the basics of function theory in one hyperbolic (split-complex, dual, duplex, motro,..) variable, perhaps the most notable being http://arxiv.org/PS_cache/math-ph/pdf/0507/0507053v2.pdf. What is covered in this and the other articles are more or less only the counterparts of most elementary topics in complex analysis. Are there really no deeper results in this theory or are they just so hard to find? If so, some links or summaries of results would be dearly appriciated.
Particularly http://clifford-algebras.org/v8/81/MOTTER81.pdf aksed for a hyperbolic equvalence of Cauchy integral formula. Thus two rather different answers were provided in http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.0375v1.pdf and http://www.springerlink.com/content/kp44rl074g7187n2 . Both articles mention immense applications that follow directly from their formulas, but I havn't been unable to find a single article discussing them.
And it is quite apparent that hyperbolic Cauchy-like formulas don't yield the percise same results as in complex analysis since it is easy to show not only that hyperbolic holomorphic functions are not allways analytic, but that they need not be even $C^2$! So could somebody explain what those mentioned direct implications of hyperbolic Cauchy formulas and also explain why are there two formulas to begin with? Thank you!