JournalszaaVol. 21, No. 2pp. 305–314

Riesz-Fischer Sequences and Lower Frame Bounds

  • Peter G. Casazza

    University of Missouri, Columbia, USA
  • Ole Christensen

    Technical University of Denmark, Lyngby, Denmark
  • Shidong Li

    San Francisco State University, USA
  • A.M. Lindner

    Technische Universität München, München Garching, Germany
Riesz-Fischer Sequences and Lower Frame Bounds cover
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Abstract

We investigate the consequences of the lower frame condition and the lower Riesz basis condition without assuming the existence of the corresponding upper bounds. We prove that the lower frame bound is equivalent to an expansion property on a subspace of the underlying Hilbert space H\mathcal H, and that the lower frame condition alone is not enough to obtain series representations on all of H\mathcal H. We prove that the lower Riesz basis condition for a complete sequence implies the lower frame condition and ω\omega-independence; under an extra condition the statements are equivalent.

Cite this article

Peter G. Casazza, Ole Christensen, Shidong Li, A.M. Lindner, Riesz-Fischer Sequences and Lower Frame Bounds. Z. Anal. Anwend. 21 (2002), no. 2, pp. 305–314

DOI 10.4171/ZAA/1079