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Frames, Riesz bases, and sampling expansions in Banach spaces via semi-inner products

Haizhang Zhang School of Mathematics and Computational Science, Sun Yat-sen University Jun Zhang University of Michigan

mathscidoc:1609.01004

Applied and Computational Harmonic Analysis, 31, (1), 1-25, 2011
Frames in a Banach space B B mathContainer Loading Mathjax were defined as a sequence in its dual space B 68 B 68 mathContainer Loading Mathjax in some recent references. We propose to define them as a collection of elements in B B mathContainer Loading Mathjax by making use of semi-inner products. Classical theory on frames and Riesz bases is generalized under this new perspective. We then aim at establishing the Shannon sampling theorem in Banach spaces. The existence of such expansions in translation invariant reproducing kernel Hilbert and Banach spaces is discussed.
Frames / Riesz bases / Bessel sequences / Riesz-Fischer sequences / Banach spaces / Semi-inner products / Duality mappings / Shannon's sampling expansions / Reproducing kernel Banach spaces / Reproducing kernel Hilbert spaces
[ Download ] [ 2016-09-20 18:20:43 uploaded by zhang ] [ 621 downloads ] [ 0 comments ] [ Cited by 19 ] 
@inproceedings{haizhang2011frames,,
  title={Frames, Riesz bases, and sampling expansions in Banach spaces via semi-inner products},
  author={Haizhang Zhang, and Jun Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160920182043698936030},
  booktitle={Applied and Computational Harmonic Analysis},
  volume={31},
  number={1},
  pages={1-25},
  year={2011},
}
Haizhang Zhang, and Jun Zhang. Frames, Riesz bases, and sampling expansions in Banach spaces via semi-inner products. 2011. Vol. 31. In Applied and Computational Harmonic Analysis. pp.1-25. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160920182043698936030.
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