Vol. 56, No. 2, 1975

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Series expansions of analytic functions. II

James Donnell Buckholtz and Ken Shaw

Vol. 56 (1975), No. 2, 373–384

This paper is concerned with series expansions of the form f(z) = 0hkpk(z), where the functions {pk} are analytic and satisfy a certain asymptotic condition. Relationships between the space of expandable functions, the coefficient space , and the matrix operator Bjk = pk(j)(0) are studied, and is shown to be a Banach space isomorphic to c0, the space of complex sequences with limit 0. Necessary and sufficient conditions for convergence of 0hkpk(z) are given in terms of the coefficient sequence h.

Mathematical Subject Classification
Primary: 30A18
Received: 11 December 1973
Published: 1 February 1975
James Donnell Buckholtz
Ken Shaw