Department of Mathematics, The University of Texas-Pan American, Edinburg, TX 78539-2999, USA
Academic Editor: Mark M. Meerschaert
Copyright © 2010 Vladimir Varlamov. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 and .
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