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dc.contributor.authorBuse, Constantin ( )
dc.contributor.authorDragomir, Sever S. ( Orcid Icon 0000-0003-2902-6805 )
dc.date.accessioned2020-07-02T22:00:20Z
dc.date.available2020-07-02T22:00:20Z
dc.date.issued2001-11-23
dc.identifier.citationBuse, C., & Dragomir, S. S. (2001). A theorem of Rolewicz's type for measurable evolution families in Banach spaces. Electronic Journal of Differential Equations, 2001(70), pp. 1-5.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/11947
dc.description.abstractLet 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.en_US
dc.formatText
dc.format.extent6 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2001, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectEvolution family of bounded linear operatorsen_US
dc.subjectEvolution operator semigroupen_US
dc.subjectRolewicz's theoremen_US
dc.subjectExponential stabilityen_US
dc.titleA Theorem of Rolewicz's Type for Measurable Evolution Families in Banach Spacesen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
dc.description.departmentMathematics


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