2025/07/07 by Victor Bailey, Bailey, Victor, Carlos Cabrelli +1
Mathematics · #Mathematical Analysis and Transform Methods #Holomorphic and Operator Theory #Advanced Harmonic Analysis Research
paper · pdf · doi:10.48550/arxiv.2507.04992
Recent work in Dynamical Sampling has been centered on characterizing frames obtained by the orbit of a vector under a bounded operator. We prove a necessary and sufficient condition for a pair of bounded commuting operators on a separable infinite-dimensional Hilbert space to generate a frame by unilateral iterations on a single vector. Applying the theory on submodules of the Hardy module H2(\mathbbT2), we characterize these frames in terms of their relation to the two-variable Jordan block on a certain quotient module and provide some properties of frames of this form.