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

Abstract EN

Riesz potentials (also called Riesz fractional derivatives) and their Hilbert transforms are computed for the Korteweg-de Vries soliton.

They are expressed in terms of the full-range Hurwitz Zeta functions ζ+(s,a) and ζ−(s,a).

It is proved that these Riesz potentials and their Hilbert transforms are linearly independent solutions of a Sturm-Liouville problem.

Various new properties are established for this family of functions.

The fact that the Wronskian of the system is positive leads to a new inequality for the Hurwitz Zeta functions.