Abstract: In this paper, the correct representation theorem and numerical calculating formulae of H^p functions suitable in the upper halp-plane are derived from the representation theorem of H^p functions in the unit disk by means of linear fractional transform.
Taking the spherical piezoelectric receiver as an example the values of its transfer function outside the given frequency range are obtained from the known values of the transfer function in the given frequency range by using the analytical continuation of H^p functions, the results are in good agreement with the theoretical values of the thansfer function.
In addition, it is shown from the formulae analysis and numerical calculation that the representation theorem of H^p functions implies the causality condition.