A New Estimation of the Growth Bound of a Periodic Evolution Family on Banach Spaces

作者：Buse Constantin^*; Khan Aftab; Rahmat Gul; Tabassum Afshan

来源：Journal of Function Spaces and Applications, 2013, 2013: 260920.

DOI：10.1155/2013/260920

Let U = {U(t,s)}(t >= s >= 0) be a strongly continuous and q-periodic evolution family acting on a complex Banach space X. We prove that if 0 < P < infinity,x epsilon X, and sup(s >= 0)sup(parallel to x parallel to <= 1) integral(infinity)(0) parallel to U(t + s,s)x parallel to(p) dt := C-p < infinity, then the growth bound of the family U is less than or equal to - 1/(pC(p)).

• 出版日期2013