ŠIMON HILSCHER, Roman and Petr ZEMÁNEK. On square integrable solutions and principal and antiprincipal solutions for linear Hamiltonian systems. Annali di Matematica Pura ed Applicata. Series IV. Berlin: Springer, 2018, vol. 197, No 1, p. 283-306. ISSN 0373-3114. Available from: https://dx.doi.org/10.1007/s10231-017-0679-7. |
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@article{1385737, author = {Šimon Hilscher, Roman and Zemánek, Petr}, article_location = {Berlin}, article_number = {1}, doi = {http://dx.doi.org/10.1007/s10231-017-0679-7}, keywords = {Linear Hamiltonian system; square integrable solution; Weyl solution; minimal principal solution at infinity; antiprincipal solution at infinity; limit point case; limit circle case}, language = {eng}, issn = {0373-3114}, journal = {Annali di Matematica Pura ed Applicata. Series IV}, title = {On square integrable solutions and principal and antiprincipal solutions for linear Hamiltonian systems}, url = {http://dx.doi.org/10.1007/s10231-017-0679-7}, volume = {197}, year = {2018} }
TY - JOUR ID - 1385737 AU - Šimon Hilscher, Roman - Zemánek, Petr PY - 2018 TI - On square integrable solutions and principal and antiprincipal solutions for linear Hamiltonian systems JF - Annali di Matematica Pura ed Applicata. Series IV VL - 197 IS - 1 SP - 283-306 EP - 283-306 PB - Springer SN - 03733114 KW - Linear Hamiltonian system KW - square integrable solution KW - Weyl solution KW - minimal principal solution at infinity KW - antiprincipal solution at infinity KW - limit point case KW - limit circle case UR - http://dx.doi.org/10.1007/s10231-017-0679-7 N2 - 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. ER -
ŠIMON HILSCHER, Roman and Petr ZEMÁNEK. On square integrable solutions and principal and antiprincipal solutions for linear Hamiltonian systems. \textit{Annali di Matematica Pura ed Applicata. Series IV}. Berlin: Springer, 2018, vol.~197, No~1, p.~283-306. ISSN~0373-3114. Available from: https://dx.doi.org/10.1007/s10231-017-0679-7.
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