A Theorem of Rolewicz's Type for Measurable Evolution Families in Banach Spaces
| dc.contributor.author | Buse, Constantin | |
| dc.contributor.author | Dragomir, Sever S. | |
| dc.date.accessioned | 2020-07-02T22:00:20Z | |
| dc.date.available | 2020-07-02T22:00:20Z | |
| dc.date.issued | 2001-11-23 | |
| dc.description.abstract | Let φ be a positive and non-decreasing function defined on the real half-line and U be a strongly measurable, exponentially bounded evolution family of bounded linear operators acting on a Banach space and satisfying a certain measurability condition as in Theorem 1 below. We prove that if φ and U satisfy a certain integral condition (see the relation 1 from Theorem 1 below) then U is uniformly exponentially stable. For φ continuous and U strongly continuous and exponentially bounded, this result is due to Rolewicz. The proofs uses the relatively recent techniques involving evolution semigroup theory. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 6 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Buse, C., & Dragomir, S. S. (2001). A theorem of Rolewicz's type for measurable evolution families in Banach spaces. <i>Electronic Journal of Differential Equations, 2001</i>(70), pp. 1-5. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/11947 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2001, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Evolution family of bounded linear operators | |
| dc.subject | Evolution operator semigroup | |
| dc.subject | Rolewicz's theorem | |
| dc.subject | Exponential stability | |
| dc.title | A Theorem of Rolewicz's Type for Measurable Evolution Families in Banach Spaces | en_US |
| dc.type | Article |