Appell polynomial expansions and biorthogonal expansions in Banach spaces

Buckholtz, J. D.

doi:10.1090/S0002-9947-1973-0333210-0

Appell polynomial expansions and biorthogonal expansions in Banach spaces
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by J. D. Buckholtz

Trans. Amer. Math. Soc. 181 (1973), 245-272

DOI: https://doi.org/10.1090/S0002-9947-1973-0333210-0

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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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