Bessel polynomial expansions in spaces of holomorphic functions
Using abstract functional analytic methods, \textit{J. Cnops} and the author [Simon Stevin 67, No. 1-2, 145-156 (1993; Zbl 0814.46002)] proved a basis criterion for nuclear power series spaces \(K(\alpha, R)\); i.e., they gave necessary and sufficient conditions for an infinite matrix \(P\) such that, with \(e_k= (\delta_{nk})_n\), \(Pe\) is a basis of \(K(\alpha,R)\). In the present paper, the author discusses how this criterion leads to a refinement of the one of B. Cannon (1937) for spaces of holomorphic functions. He then utilizes it to derive that the sequence of Bessel polynomials is an effective basis in the space \({\mathcal O}(B(R))\) of holomorphic functions on the disk of radius \(R\), \(0<R<\infty\). -- There are some obvious misprints.
scientific article; zbMATH DE number 1215645