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The $\mathrm{U}$-Derivative Associated with Linear Recurrence Sequences
We associate a canonical operator to every linear recurrence sequence admitting a distinct-root Binet representation \(\mathrm{U}_n=\sum_{j=1}^{k}A_jλ_j^n.\) The construction is based on the spectral Binet operator \(\mathcal{B}_\mathrm{U}=\sum_{j=1}^{k}A_jT_{λ_j}, \) where \(T_{λ_j}f(x)=f(λ_jx)\) i
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