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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |