On square integrable solutions and principal and antiprincipal solutions for linear Hamiltonian systems
| Autor: | Roman Šimon Hilscher, Petr Zemánek |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Circular points at infinity
Applied Mathematics 010102 general mathematics Mathematical analysis 01 natural sciences Square (algebra) Connection (mathematics) Hamiltonian system 010101 applied mathematics Square-integrable function Limit point Point at infinity 0101 mathematics Hamiltonian (control theory) Mathematics |
| Zdroj: | Annali di Matematica Pura ed Applicata (1923 -). 197:283-306 |
| ISSN: | 1618-1891 0373-3114 |
| DOI: | 10.1007/s10231-017-0679-7 |
| Popis: | New results in the Weyl–Titchmarsh theory for linear Hamiltonian differential systems are derived by using principal and antiprincipal solutions at infinity. In particular, a non-limit circle case criterion is established and a close connection between the Weyl solution and the minimal principal solution at infinity is shown in the limit point case. In addition, the square integrability of the columns of the minimal principal solution at infinity is investigated. All results are obtained without any controllability assumption. Several illustrative examples are also provided. |
| Databáze: | OpenAIRE |
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