2018/06/01 by Gen Wang, Wang, Gen
Mathematics · #32V05 #32W05 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32V05 #msc:32W05
paper · pdf · doi:10.48550/arxiv.1806.00171
20 pages
arxiv created 2020/02/20 · arxiv updated 2020/02/21
This paper aims at studying a functional K-transformation w( z )→ \widetildew( z )=w( z )K( z ) that is made to reconsider the complex differentiability for a given complex function w and subsequently we obtain structural holomorphic to judge a complex function to be complex structural differentiable. Since K( z ) can be chosen arbitrarily, thus it has greatly generalized the applied practicability. And we particularly consider K ( z )= 1+κ( z ), then we found an unique Carleman-Bers-Vekua equations which is more simpler that all coefficients are dependent to the structural function κ( z ). The generalized exterior differential operator and the generalized Wirtinger derivatives are simultaneously obtained as well. As a discussion, second-order nonlinear Laplace equation is studied.