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$L^p$-continuity for discrete linear causal systems

Let $p \in [1, +\infty)$, $(b_0(n)), \dots (b_m(n)), (a_1(n)), \dots, (a_m(n))$ suitable sequences of real numbers and consider the map $\phi: \ell^p \to \ell^p$, $x \mapsto y$ defined by: \begin{...