Riesz Potentials for Korteweg-de Vries Solitons and Sturm-Liouville Problems
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 ar...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2010/193893 |
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| Summary: | 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. |
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| ISSN: | 1687-9643 1687-9651 |