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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Appell polynomial expansions and biorthogonal expansions in Banach spaces

Author: J. D. Buckholtz
Journal: Trans. Amer. Math. Soc. 181 (1973), 245-272
MSC: Primary 30A98; Secondary 46E15
MathSciNet review: 0333210
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Abstract: Let $ \{ {p_k}\} _0^\infty $ denote the sequence of Appell polynomials generated by an analytic function $ \phi $ with the property that the power series for $ \theta = 1/\phi $ has a larger radius of convergence than the power series for $ \phi $. The expansion and uniqueness properties of $ \{ {p_k}\} $ are determined completely. In particular, it is shown that the only convergent $ \{ {p_k}\} $ expansions are basic series, and that there are no nontrivial representations of 0. An underlying Banach space structure of these expansions is also studied.

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Keywords: Appell polynomials, polynomial expansions, basic series, biorthogonal expansions, bases in Banach spaces
Article copyright: © Copyright 1973 American Mathematical Society