Admissible data for a periodic convolution inverse
= Admissible data for a periodic convolution inverse
{title2=$\sum_n|y_n/c_n|^2<\infty$}
When all multipliers are nonzero, the <Moore–Penrose inverse of an operator> acts by dividing each <Fourier coefficient> $y_n$ by $c_n$. Its data domain is precisely the square-summability condition displayed. The dense range need not be closed, and writing the formal inverse series does not establish the <Picard criterion>.