Parseval quasi-dual frames

G. CORACH; P. MASSEY; M. RUIZ

Nashville, TN

Conferencia; 5º International Conference on Computational Harmonic Analysis; 2014

Let  $\{f_i\}_{i\in I}$  and $\{g_i\}_{i\in I} be pair of  frames for a Hilbert space $H$, with synthesis operators $F$ and $X$ respectively . In this talk, we discuss some results concerning the computation of the infimum of the operator norm of $FX^*-I$, where $\{g_i}_{i\in I}$   is any Parseval frame. In some sense, this quantity measures the (normalized) worst-case error in the reconstruction of vectors when analyzed with the Parseval frame  and synthesized with $\{f_i\}_{i\in I}$. In case that the infimum is attained on a Parseval frame $\{g_i\}_{i\in I}, we call it a  quasi-dual of $\{f_i\}_{i\in I}. This talk  is based on joint work with Pedro Massey (UNLP-IAM, Argentina) and Gustavo Corach (UBA-IAM, Argentina).