Highly Influential

Let f (n)n = 0, ? 1, ?2, ... be a sequence of complex valued functions on the real line with (d/dx)f(n) = f(n+l) and satisfying inequalities If (n)(x) I < Mn (1 + IXI)k where as n -X oo the growth conditions lim Mn (1 + ,)-n = 0 and limM-n(1 + e)-n = 0 hold for all e > 0. Then f(0)(x) = p(x)eix + q(x)e-ix where p and q are polynomials of degree at most k… (More)