Open Access
January 2017 Frames and representing systems in Fréchet spaces and their duals
J. Bonet, C. Fernández, A. Galbis, J. M. Ribera
Banach J. Math. Anal. 11(1): 1-20 (January 2017). DOI: 10.1215/17358787-3721183


Frames and Bessel sequences in Fréchet spaces and their duals are defined and studied. Their relation with Schauder frames and representing systems is analyzed. The abstract results presented here, when applied to concrete spaces of analytic functions, give examples and consequences about sampling sets and Dirichlet series expansions.


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J. Bonet. C. Fernández. A. Galbis. J. M. Ribera. "Frames and representing systems in Fréchet spaces and their duals." Banach J. Math. Anal. 11 (1) 1 - 20, January 2017.


Received: 13 July 2015; Accepted: 12 February 2016; Published: January 2017
First available in Project Euclid: 19 October 2016

zbMATH: 1369.46002
MathSciNet: MR3562358
Digital Object Identifier: 10.1215/17358787-3721183

Primary: 46A04
Secondary: 42C15 , 46A13 , 46E10

Keywords: $(LB)$-spaces , frames , Fréchet spaces , representing systems , weakly sufficient sets

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 1 • January 2017
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