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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832559188314685440 |
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| author | Vladimir Varlamov |
| author_facet | Vladimir Varlamov |
| author_sort | Vladimir Varlamov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0ccab0afc7c245cc9b48d6c2d2b4a2d1 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-0ccab0afc7c245cc9b48d6c2d2b4a2d12025-02-03T01:30:36ZengWileyInternational Journal of Differential Equations1687-96431687-96512010-01-01201010.1155/2010/193893193893Riesz Potentials for Korteweg-de Vries Solitons and Sturm-Liouville ProblemsVladimir Varlamov0Department of Mathematics, The University of Texas-Pan American, Edinburg, TX 78539-2999, USARiesz 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.http://dx.doi.org/10.1155/2010/193893 |
| spellingShingle | Vladimir Varlamov Riesz Potentials for Korteweg-de Vries Solitons and Sturm-Liouville Problems International Journal of Differential Equations |
| title | Riesz Potentials for Korteweg-de Vries Solitons and Sturm-Liouville Problems |
| title_full | Riesz Potentials for Korteweg-de Vries Solitons and Sturm-Liouville Problems |
| title_fullStr | Riesz Potentials for Korteweg-de Vries Solitons and Sturm-Liouville Problems |
| title_full_unstemmed | Riesz Potentials for Korteweg-de Vries Solitons and Sturm-Liouville Problems |
| title_short | Riesz Potentials for Korteweg-de Vries Solitons and Sturm-Liouville Problems |
| title_sort | riesz potentials for korteweg de vries solitons and sturm liouville problems |
| url | http://dx.doi.org/10.1155/2010/193893 |
| work_keys_str_mv | AT vladimirvarlamov rieszpotentialsforkortewegdevriessolitonsandsturmliouvilleproblems |