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Matrix Mean Series in Terms of Boundary Orthogonal Systems and Functions in the Classes Hinfin and Ep

We give conditions for orthonormal systems on the boundary of a plane Jordan domain which are necessary and sufficient for an arbitrary series in terms of this orthonormal system to be the Fourier series of some function in H∞(G) resp. EP(G)(1 < p < ∞). Our results contain a classical criterion of Fejer for the boundedness of a holomorphic function in the unit disk.