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analytic functions approximated arbitrary assume Bergman boundary value problems bounded Cauchy data coefficients Colton compact complete family complex variables Consequently consider constant continuous converges uniformly CR-holomorphic Definition Dirichlet problem Douglis dt(C E-function elliptic equations elliptic systems exists family of solutions fF,G formula Fredholm equations Furthermore given Goursat data Goursat problem harmonic functions harmonic polynomials hence holomorphic functions hyperanalytic function hypercomplex functions hypercomplex number Icl-i implies inequality initial conditions integral equation integral representation introduce kernels Lemma linear mapping neighborhood obtain pair partial differential equation plane pluriharmonic functions plurisubharmonic points polydisk possible singularities Proof real hypercomplex recursive regular domain Remark Riemann function satisfy seek a solution sequence shown simply-connected solution of 2.28 space subharmonic Theorem Tjong unique solution uniquely determined vanishes Vekua Verify zero