Generalized Growth and Approximation of Pseudoanalytic Functions on the Disk

Abstract

McCoy [20] considered the approximation of pseudoanalytic functions (PAF) on the disk. Pseudoanalytic functions are constructed as complex combination of real - valued analytic solutions to the Stokes-Beltrami System. These solutions include the generalized biaxisymmetric potentials. McCoy obtained some coecient and Bernstein type growth theorems on the disk. The aim of this paper is to generalize the results of McCoy [20]. Moreover, we study the generalized order and generalized type of PAF in terms of Fourier coecients occurring in its local expansion and optimal approximation errors in Bernstein sense on the disk. Our approach and method are dierent from those of McCoy [20].