Pseudoholomorphic functions with nonantiholomorphic characteristics

Abstract

Let κ ( z ) ∈ C ∞ ( Ω ) \kappa (z) \in {C^\infty }(\Omega ) and ‖ κ ‖ > 1 \left \| \kappa \right \| > 1 . Necessary and sufficient conditions for the system of equations ∂ f ¯ = κ ( z ) ∂ f \partial \bar f = \kappa (z)\partial f to be locally plentiful are given, and under them a representation of κ \kappa also is given.