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Journal of the London Mathematical Society 1980 s2-21(3):487-495; doi:10.1112/jlms/s2-21.3.487
© 1980 by London Mathematical Society
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© Oxford University Press

Abel–Goncarov Polynomial Expansions in Spaces of Holomorphic Functions

Friedrich Haslinger

Institut für Mathematik, Universität Wien Strudlhofgasse 4, A–1090 Wien, Austria

In this paper we give a characterization of those sequences for which the respective Abel–Goncarov polynomials constitute a basis in the space fR of holomorphic functions on the disc |z| < R (0 < R ≤ {infty}). General methods of nuclear Fréchet spaces in conjunction with the theory of Köthe-sequence spaces are used to obtain the necessary and sufficient conditions.


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