Quasicontraction semigroup

In mathematical analysis, a "C"0-semigroup Γ("t"), "t" ≥ 0, is called a quasicontraction semigroup if there is a constant "ω" such that ||Γ("t")|| ≤ exp("ωt") for all "t" ≥ 0. Γ("t") is called a contraction semigroup if ||Γ("t")|| ≤ 1 for all "t" ≥ 0.