## Elliptic systems in the plane |

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2-a dgdn 2iri w(C 2TTi analytic continuation analytic functions analytic in G bounded in G Cauchy integral representation complex valued function component conclude converges absolutely converges uniformly Corollary d?dn d£dn z=z dCdn Define V(z Definition denote differentiable disk Dnw(z domain G Douglis dt(C dt(s dt(z Dw(z equation Fubini's theorem functions f fundamental kernels Gilbert-Hile Green's identity Hence Holder continuous hyperanalytic function hyperanalytic in G hypercomplex function hypercomplex number ImX(z J_ Dv Lemma Let G Let w(z Liouville's theorem LP(G matrix nilpotent null space Pompieu operator preceding theorem previous theorem product rule proves Q is quasidiagonal Qw(z regular domain Removable Singularities right hand side satisfies solution of 24 t(zQ t(zQ+h tc(c tz(z uniformly and absolutely vanishes at infinity Vekua z e G z-zQ