Invertibility and dichotomy of differential operators on a half-line |
| |
| Authors: | A Ben-Artzi I Gohberg M A Kaashoek |
| |
| Institution: | (1) Department of Mathematics, Indiana University, Swain East 222, 47405 Bloomington, Indiana;(2) Raymond and Beverly Sackler Faculty of Exact Science, School of Mathematical Sciences, Tel Aviv University, Ramat-Aviv, Israel;(3) Department of Mathematics and Computer Science, Vrije Universiteit, Amsterdam, The Netherlands |
| |
| Abstract: | A linear ordinary differential operator with bounded coefficients satisfying certain homogeneous initial conditions is shown to be invertible onL
n
2
(0,  ) if and only if the underlying system of differential equations has a dichotomy. Moreover, in that case the operator is proved to be a direct sum of two infinitesimal generators ofC
0-semigroups, one of which has support on the negative half-line and the other on the positive half-line. The effect of perturbations of the initial values on the dichotomy is also described. |
| |
| Keywords: | Dichotomy differential operator invertibility C
0-semigroup perturbation |
| 本文献已被 SpringerLink 等数据库收录！ |
|
