Buse, ConstantinNguyen, Thanh LanO'Regan, Donal2022-03-102022-03-102018-11-20Buşe, C., Nguyen, L. T., & O'Regan, D. (2018). Global and local versions for a Phong Vu theorem for periodic evolution families in Hilbert spaces. <i>Electronic Journal of Differential Equations, 2018</i>(188), pp. 1-12.1072-6691https://hdl.handle.net/10877/15484A theorem of Gearhart concerning strongly continuous semigroups in Hilbert spaces is extremely useful for stability analysis of concrete equations; see e.g. [20]), and for control theory [27] or [13, page 475]. Phong Vu introduced an equivalent condition in [23]. The aim of this article is to extend these results from the autonomous case to time dependent 1-periodic evolution equations in Hilbert spaces. Both cases (continuous and discrete) are analyzed and global and local versions of the Phong Vu theorem are provided.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalUniform exponential stabilityGrowth boundsFourier seriesExponentially bounded evolution families of operatorsArticle