ŠEPITKA, Peter and Roman ŠIMON HILSCHER. Reid's construction of minimal principal solution at infinity for linear Hamiltonian systems. In S. Pinelas, Z. Došlá, O. Došlý, P.E. Kloeden. Differential and Difference Equations with Applications: ICDDEA, Amadora, Portugal, May 2015, Selected Contributions. NEW YORK: Springer, 2016, p. 359-369. ISBN 978-3-319-32855-3. Available from: https://dx.doi.org/10.1007/978-3-319-32857-7_34. |
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@inproceedings{1309080, author = {Šepitka, Peter and Šimon Hilscher, Roman}, address = {NEW YORK}, booktitle = {Differential and Difference Equations with Applications: ICDDEA, Amadora, Portugal, May 2015, Selected Contributions}, doi = {http://dx.doi.org/10.1007/978-3-319-32857-7_34}, editor = {S. Pinelas, Z. Došlá, O. Došlý, P.E. Kloeden}, keywords = {Linear Hamiltonian system; Principal solution at infinity; Antiprincipal solution at infinity; Minimal principal solution at infinity; Controllability; Moore-Penrose pseudoinverse}, howpublished = {tištěná verze "print"}, language = {eng}, location = {NEW YORK}, isbn = {978-3-319-32855-3}, pages = {359-369}, publisher = {Springer}, title = {Reid's construction of minimal principal solution at infinity for linear Hamiltonian systems}, url = {http://www.springer.com/gp/book/9783319328553}, year = {2016} }
TY - JOUR ID - 1309080 AU - Šepitka, Peter - Šimon Hilscher, Roman PY - 2016 TI - Reid's construction of minimal principal solution at infinity for linear Hamiltonian systems PB - Springer CY - NEW YORK SN - 9783319328553 KW - Linear Hamiltonian system KW - Principal solution at infinity KW - Antiprincipal solution at infinity KW - Minimal principal solution at infinity KW - Controllability KW - Moore-Penrose pseudoinverse UR - http://www.springer.com/gp/book/9783319328553 N2 - Recently the authors introduced a theory of principal solutions at infinity for nonoscillatory linear Hamiltonian systems in the absence of the complete controllability assumption. In this theory the so-called minimal principal solution at infinity plays a distinguished role (the minimality refers to the rank of the first component of the solution). In this paper we show that the minimal principal solution at infinity can be obtained by a suitable generalization of the Reid construction of the principal solution known in the controllable case. Our new result points to some applications of the minimal principal solution at infinity e.g. in the spectral theory of linear Hamiltonian systems. ER -
ŠEPITKA, Peter and Roman ŠIMON HILSCHER. Reid's construction of minimal principal solution at infinity for linear Hamiltonian systems. In S. Pinelas, Z. Došlá, O. Došlý, P.E. Kloeden. \textit{Differential and Difference Equations with Applications: ICDDEA, Amadora, Portugal, May 2015, Selected Contributions}. NEW YORK: Springer, 2016, p.~359-369. ISBN~978-3-319-32855-3. Available from: https://dx.doi.org/10.1007/978-3-319-32857-7\_{}34.
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