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Dynamical Sampling Associated with the Fractional Fourier Transform

In this paper, we mainly study the dynamical sampling of sequence spaces and shift-invariant spaces in the fractional Fourier transform domains. We show that how to recover the signals in sequence spaces or shift-invariant spaces from their dynamical sampling values. We provide a necessary and sufficient condition for the dynamical sampling problem of sequence spaces and shift-invariant spaces in the fractional Fourier transform domains to be solvable. Our results generalize similar ones in the Fourier transform domains.