Hankel integral operators and isometric interpolants on the line

The problem of finding an m × n continuous isometric matrix valued function with entries from the Wiener algebra on the line and with prespecified Fourier inverse transform on the half line is studied. Conditions for existence, uniqueness, and formulas for the solution of this problem are presented. Connections are made between the positive factorization indices of certain solutions to this problem and the dimensions of the kernels of Hankel operators based on the prespecified data alluded to above. The paper uses techniques and results developed in an earlier study of an interpolation problem on the circle. The main theorems are in fact continuous analogues of the latter.