  The dispersive representation of the virtual Compton forward scattering
amplitude has been recently reexamined in connection with the evaluation of the
Cottingham formula for the proton-neutron electromagnetic mass difference. The
most difficult part of the analysis is related to one of the invariant
amplitudes, denoted as $T_1(\nu, Q^2)$, which requires a subtraction in the
standard dispersion relation with respect to the energy $\nu$ at fixed photon
momentum squared $q^2=-Q^2$. We propose an alternative dispersive framework,
which implements analyticity and unitarity by combining the Cauchy integral
relation at low and moderate energies with the modulus representation of the
amplitude at high energies. Using techniques of functional analysis, we derive
a necessary and sufficient condition for the consistency with analyticity of
the subtraction function $S_1(Q^2)=T_1(0, Q^2)$, the electron-proton cross
sections measured at low and moderate energies and the Regge model assumed to
be valid at high energies. From this condition we obtain model-independent
constraints on the subtraction function, confronting them with the available
information on nucleon magnetic polarizabilities and results reported recently
in the literature. The formalism can be used also for testing the existence of
a fixed pole at $J=0$ in the angular momentum plane, but more accurate data are
necessary for a definite answer.
