Infinitely many equations with infinitely many unknowns Let $$d_n=\sum_{m=1}^{\infty}a_ma_{m+n}$$ then can we find $\{a_n\}$ in terms of $\{d_n\}$? I appreciate any hints :-)


All values are real. 
In general I am interested in $d_n$ such that $d_n \to 0$ and in general $d_n \neq 0$.
$\sum d_n &lt; \infty$.
Not necessarily uniquely.

For example $d_0=1$ and $d_n=0$ for $n \not = 0$ can be generated by 

\begin{equation}
    a_m=
    \begin{cases}
      \pm1, &amp; \text{if}\ m=k \\
      0, &amp; \text{otherwise}
    \end{cases}
  \end{equation}

given any positive integer $k$
Not necessarily uniquely.

For example $d_0=1$ and $d_n=0$ for $n \not = 0$ can be generated by 

\begin{equation}
    a_m=
    \begin{cases}
      \pm1, &amp; \text{if}\ m=k \\
      0, &amp; \text{otherwise}
    \end{cases}
  \end{equation}

given any positive integer $k$