Every frame in Hilbert space contains a subsequence equivalent to an orthogonal basis. If a frame is n-dimensional then this subsequence has length (1 − ε)n. On the other hand, there is a frame which does not contain bases with brackets.

We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building on a geometric formula for the analysis operator defined from F . Our focus is on the infinite-dimensional case where a priori estimates play a central role, ...

In this paper we establish a surprising new identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss the derived results.

We make a deep study of the distance between frames and between subspaces of a Hilbert space. There are many surprises here. First, of the six standard ways of measuring distance between subspaces, 5 of them are equal and the sixth, chordal distance, is within a factor of 2 of the others. We also show that the vectors giving chordal distance are biorthogonal which the definition does not indica...

We prove that any tight frame in Hilbert space can be obtained by the Kaczmarz algorithm. An explicit way of constructing this correspondence is given. The uniqueness of the correspondence is determined.

Large-scale structures are often built using space frames or trusses. These can become complex if the geometry of frame structure is customizable and they do not contain any recurring components. Consequently, design effort required, production cost these unique components large. Further, designing creating challenging for novice designers as processes require large know-how. This challenge be ...