Introduction. In a series of papers [3], [4], [6], we studied the relationship between two closed subspaces of L2(c, co): the subspace 22T of all f C L2 supported in ItI < T/2 and the subspace M,n of all f E L2 whose Fourier transforms are supported in IcI < Q/2. We showed that several questions about 22T and M,, could be answered in terms of the eigenvalues of the operator BnDTBn, where Bn and DT are the projections onto -A, and 29 Trespectively; this operator may be written as a finite convolution. Apart from this application, interpretable as describing the way in which the energy of a function of L2 can be distributed over time and over frequency, the behavior of these eigenvalues is interesting because it differs markedly from that established by H. Widom [7] for the class of finite convolutions with L' kernels whose Fourier transforms have an absolute maximum at the origin. By a change of variable, the eigenvalues of BnDTBn may be seen to depend on the parameter c = uT/2wr, rather than on Q and T separately; we may write their equation explicitly as