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.


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


Zbl 0814.46002
Full Text: DOI


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