The Hermite Property of a Causal Wiener Algebra Used in Control Theory

Let \mathbbC₊ : = {s ? \mathbbC    |     Re(s) 3 0}{{\mathbb{C}}}_{+} := \{s \in {{\mathbb{C}}}\quad | \quad {\rm Re}(s) \geq 0\} and let A\mathcal{A} denote the Banach algebra

A = { s( ? \mathbbC+ ) ? ^(f)]a (s) + ?k = 0￥ fk e - stk | lfa ? L1 (0,￥),(fk )k 3 0 ? l1, 0 = t0 < t1 < t2 < ? }{{{\mathcal{A}}}} = \left\{ s( \in {{{\mathbb{C}}}}_ + ) \mapsto \hat{f}_a (s) + \sum\limits_{k = 0}^\infty {f_k e^{ - st_k }}\bigg | \bigg.{\begin{array}{l}{f_a \in L^1 (0,\infty ),(f_k )_{k \geq 0} \in \ell^{1}, } \cr {{0 = t_0 < t_1 < t_2 < \ldots}} \end{array}} \right\}
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