In this paper we consider two problems in frame theory. On the one hand, given a set of vectors F we describe the spectral and geometrical structure of optimal completions of F by a finite family of vectors with prescribed ...

Given a finite sequence of vectors F0 in a d-dimensional complex Hilbert space H we characterize in a complete and explicit way the optimal completions of F0 obtained by appending a finite sequence of vectors with prescribed ...

Let H be a finite dimensional (real or complex) Hilbert space and let {a_i} ∞_i=1. be a non-increasing sequence of positive numbers. Given a finite sequence of vectors F = {f_i}p_i=1 in H we find necessary and sufficient ...

Let F0 = {fi}i∈In0 be a finite sequence of vectors in Cd and let a = (ai)i∈Ik be a finite sequence of positive numbers, where In = {1,...,n} for n ∈ N. We consider the completions of F0 of the form F = (F0, G) obtained by ...

Given a finite sequence of vectors F0 in C d we describe the spectral and geometrical structure of optimal frame completions of F0 obtained by appending a finite sequence of vectors with prescribed norms, where optimality ...

In this note, we prove some results related to small perturbations of a frame for a Hilbert space H in order to have a woven pair for H. Our results complete those known in the literature. In addition we study a necessary ...