Hille–Yosida type theorems for -times integrated semigroups

作者：Zhanrong Hu; Zhen Jin

来源：Nonlinear Analysis-Theory Methods & Applications, 2009, 71(1–2): 521-530.

• n
• -times integrated Laplace transforms
• O(ω(t))
• vector-valued functions
• O(ω(t))n
• -times integrated semigroups
• Infinitesimal generators
• Hille–Yosida type theorems

For an arbitrary continuous increasing function ω(t):[0,∞)↦C, we introduce the concept and characterize the properties of n-times integrated Laplace transforms of O(ω(t)) vector-valued functions. Based on these properties, we have established Hille–Yosida type theorems for O(ω(t))n-times integrated semigroups. An explanation example is given.