Generalized frame operator, lower semiframes, and sequences of translates

Rosario Corso

Mathematische Nachrichten, 2023, vol. 296, issue 7, 2715-2733

Abstract: Given an arbitrary sequence of elements ξ={ξn}n∈N$\xi =\lbrace \xi _n\rbrace _{n\in \mathbb {N}}$ of a Hilbert space (H,⟨·,·⟩)$(\mathcal {H},\langle \cdot ,\cdot \rangle )$, the operator Tξ$T_\xi$ is defined as the operator associated to the sesquilinear form Ωξ(f,g)=∑n∈N⟨f,ξn⟩⟨ξn,g⟩$\Omega _\xi (f,g)=\sum _{n\in \mathbb {N}} \langle f , \xi _n\rangle \langle \xi _n , g\rangle$, for f,g∈{h∈H:∑n∈N|⟨h,ξn⟩|2

Date: 2023
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