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Matrix Mean Series in Terms of Boundary Orthogonal Systems and Functions in the ClassesH ∞andEp

Authors
Journal
Journal of Approximation Theory
0021-9045
Publisher
Elsevier
Publication Date
Volume
118
Issue
2
Identifiers
DOI: 10.1006/jath.2002.3720

Abstract

Abstract 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. E P(G )(1< p<∞). Our results contain a classical criterion of Fejér for the boundedness of a holomorphic function in the unit disk.

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