Vol. 84, No. 1, 1979

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A dual relationship between generalized Abel-Gončarov bases and certain Pincherle bases

Friedrich Haslinger

Vol. 84 (1979), No. 1, 79–90

Recent results on Abel-Gončarov polynomial expansions are applied to study the representability of holomorphic functions as infinite series in a given Pincherle sequence. As a generalization of the ordinary derivative we consider the so-called Gel’fond-Leont’ev derivative 𝒟. We take the exponential function with respect to the derivative 𝒟 and use a duality principle in order to investigate the completeness of the system En(z) = znE(λnz) in the space r of functions holomorphic on the interior of the disc of radius r . Finally we study the uniqueness of the representability of holomorphic functions as infinite series in the system En.

Mathematical Subject Classification 2000
Primary: 46A35
Secondary: 30B60, 46E10
Received: 7 July 1978
Published: 1 September 1979
Friedrich Haslinger