Riesz Potentials for Korteweg-de Vries Solitons and Sturm-Liouville Problems

Riesz potentials (also called Riesz fractional derivatives) and their Hilberttransforms are computed for the Korteweg-de Vries soliton. They are expressedin terms of the full-range Hurwitz Zeta functions +(,) and −(,). It is proved that these Riesz potentials and their Hilbert transforms are linearlyindependent solutions of a Sturm-Liouville problem. Various newproperties are established for this family of functions. The fact that theWronskian of the system is positive leads to a new inequality for the HurwitzZeta functions