The problems in Harold Walker’s latest essay, amusingly titled “The Facts of Life”, start with his very first line: Digital Modulation is usually a form of pulse modulation, of which, there are two types-Pulse Width and Pulse position. What about pulse amplitude modulation (PAM), phase shift keying (PSK) and frequency shift keying (FSK), just to mention a few others? All pulses are analyzed by ...

In this article we prove that if the coefficients of a Fourier–Legendre expansion satisfy a suitable Hausdorff–type condition, then the series converges to a function which admits a holomorphic extension to a cut–plane. Furthermore, we prove that a Laplace–type (Laplace composed with Radon) transform of the function describing the jump across the cut is the unique Carlsonian interpolation of th...