1. Main theorem. Let x = (xo, xi, • • • ) be a sequence of complex numbers and let | x \ he the norm | x | = (^Z | x„ |2)1/2 2:0. Let an asterisk denote complex conjugation. If \x\ < <» and |y| < oo, let [x, y] = [y, x] denote the sum of the series ^T,xnyn, that is, the "scalar" product of y by x*. For a given x with a finite norm |x|, let x(t) denote a function of class i2(0, 27r) having the F...