Recovering Bicomplex Holomorphic Functions Without Cauchy-Riemann Equations

Recovering Bicomplex Holomorphic Functions Without Cauchy-Riemann Equations

Explore the intricacies of recovering bicomplex holomorphic functions without using Cauchy-Riemann equations in this 28-minute seminar talk by Lino F. Resendis Ocampo. Delve into an alternative proof of Ahlfors' classical statement on reconstructing holomorphic functions from their real or imaginary parts. Examine the concept of complex harmonic functions and their relationship to bicomplex holomorphic theory. Learn how to recover a complex conjugate harmonic function V from a given complex harmonic function U, resulting in a bicomplex holomorphic function U + jV. Gain insights into the algebra, geometry, and analysis of bicomplex holomorphic functions, drawing from key references in complex analysis and bicomplex function theory.