Frames and pseudo-inverses
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.
scientific article; zbMATH DE number 861771