Christensen, Ole Frames and pseudo-inverses. (English) Zbl 0845.47002 J. Math. Anal. Appl. 195, No. 2, 401-414 (1995). A family \(\{f_i \}_{i\in I}\) in an infinite-dimensional Hilbert space \({\mathcal H}\) is called a Bessel sequence if \(\forall_{f\in {\mathcal H}} \sum_{i\in I} |\langle f,f_i \rangle|^2< \infty\). A Bessel sequence \(\{f_i \}_{i\in I}\) is called a frame if \[ \exists A>0:\;A|f|^2\leq \sum_{i\in I}|\langle f,f_i \rangle|^2, \qquad \forall f\in {\mathcal H}. \] There are studied connections between the frame theory and the theory of pseudo-inverse operators (i.e. Moore-Penrose inverses). According to the author, the frame theory is now a very useful tool in the wavelet theory. Reviewer: D.Przeworska-Rolewicz (Warszawa) Cited in 42 Documents MSC: 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A30 Norms (inequalities, more than one norm, etc.) of linear operators 42C15 General harmonic expansions, frames Keywords:Bessel sequence; frame; pseudo-inverse operators; Moore-Penrose inverses; wavelet theory PDF BibTeX XML Cite \textit{O. Christensen}, J. Math. Anal. Appl. 195, No. 2, 401--414 (1995; Zbl 0845.47002) Full Text: DOI OpenURL