We generalize some theorems of Titchmarsh on the positivity of Fourier sine and cosine integrals to the case of integral transforms with more general functions , and use them to prove the absence of positive eigenvalues - i.e. eigenvalues embeded in the continuum - for the Schrödingr equation with nonlocal separable potentials. Such nonlocal potentials are of current use in few-body problems in Nuclear Physics.

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