Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems
We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time scale 𝕋, which allows one to treat both continuous and discrete linear Hamiltonian systems as special cases for 𝕋=ℝ and 𝕋=ℤ within one theory and to explain the discr...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/514760 |
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| _version_ | 1832551571475398656 |
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| author | Shurong Sun Martin Bohner Shaozhu Chen |
| author_facet | Shurong Sun Martin Bohner Shaozhu Chen |
| author_sort | Shurong Sun |
| collection | DOAJ |
| description | We establish the Weyl-Titchmarsh theory for singular linear
Hamiltonian dynamic systems on a time scale 𝕋, which allows one to treat both continuous
and discrete linear Hamiltonian systems as special cases for 𝕋=ℝ and 𝕋=ℤ within one
theory and to explain the discrepancies between these two theories. This paper extends the
Weyl-Titchmarsh theory and provides a foundation for studying spectral theory of Hamiltonian dynamic systems. These investigations are part of a larger program which includes
the following: (i) M(λ) theory for singular Hamiltonian systems, (ii) on the spectrum
of Hamiltonian systems, (iii) on boundary value problems for Hamiltonian dynamic systems. |
| format | Article |
| id | doaj-art-ebd587a93e0c49fe9178d91e1f194fb2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ebd587a93e0c49fe9178d91e1f194fb22025-02-03T06:01:10ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/514760514760Weyl-Titchmarsh Theory for Hamiltonian Dynamic SystemsShurong Sun0Martin Bohner1Shaozhu Chen2School of Science, University of Jinan, Jinan, Shandong 250022, ChinaDepartment of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USADepartment of Mathematics, Shandong University in Weihai, Weihai, Shandong 264209, ChinaWe establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time scale 𝕋, which allows one to treat both continuous and discrete linear Hamiltonian systems as special cases for 𝕋=ℝ and 𝕋=ℤ within one theory and to explain the discrepancies between these two theories. This paper extends the Weyl-Titchmarsh theory and provides a foundation for studying spectral theory of Hamiltonian dynamic systems. These investigations are part of a larger program which includes the following: (i) M(λ) theory for singular Hamiltonian systems, (ii) on the spectrum of Hamiltonian systems, (iii) on boundary value problems for Hamiltonian dynamic systems.http://dx.doi.org/10.1155/2010/514760 |
| spellingShingle | Shurong Sun Martin Bohner Shaozhu Chen Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems Abstract and Applied Analysis |
| title | Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems |
| title_full | Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems |
| title_fullStr | Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems |
| title_full_unstemmed | Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems |
| title_short | Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems |
| title_sort | weyl titchmarsh theory for hamiltonian dynamic systems |
| url | http://dx.doi.org/10.1155/2010/514760 |
| work_keys_str_mv | AT shurongsun weyltitchmarshtheoryforhamiltoniandynamicsystems AT martinbohner weyltitchmarshtheoryforhamiltoniandynamicsystems AT shaozhuchen weyltitchmarshtheoryforhamiltoniandynamicsystems |