Hille-Yosida type theorems for \(O(\omega (t))n\)-times integrated semigroups
For an arbitrary continuous increasing function \(\omega(t):[0,\infty )\to \mathbb C\), the authors introduce the concept of \(n\)-times integrated Laplace transforms of \(O(\omega (t))\) vector-valued functions, taking into account fundamental contributions due to Arendt, Kellermann and Hieber. The authors characterize the properties of the above integrated Laplace transforms. Thanks to these properties, they establish Hille-Yosida type theorems for \(O(\omega (t))n\)-times integrated semigroups. An example of application of this theory is given at the end of the paper.
\(n\)-times integrated Laplace transforms
\(O(\omega (t))\) vector-valued functions
\(O(\omega (t))n\)-times integrated semigroups
scientific article; zbMATH DE number 5563055