A COUNTEREXAMPLE ON CONTINUOUS COPRIME FACTORS

In [1], the following question was raised: Consider a linear, shift-in variant system on L2[0, infinity). Let the graph of the system have Fo urier transform (M/N) H-2 (i.e., the system has a transfer function P = N/M) where M, N are elements of C(A) = {f is-an-element-of H(infinit y): f is continuous on the compactified right-half plane}. Is it possi ble to normalize M and N (i.e., to ensure \M\2 + \N\2 = 1) in C(A)? He re, we show by example that this is not always possible.