Bessel polynomial expansions in spaces of holomorphic functions. (English) Zbl 0913.46003
Using abstract functional analytic methods, 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.
Reviewer: Klaus Dieter Bierstedt (Paderborn)
MSC:
| 46A35 | Summability and bases in topological vector spaces |
| 46A11 | Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) |
| 46E10 | Topological linear spaces of continuous, differentiable or analytic functions |
| 46A04 | Locally convex Fréchet spaces and (DF)-spaces |
Keywords:
basis transform; polynomial basis; basis criterion; nuclear power series spaces; spaces of holomorphic functions; Bessel polynomials; effective basisCitations:
Zbl 0814.46002References:
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