On analytic semigroups and cosine functions in Banach spaces
Tom 129 / 1998
Studia Mathematica 129 (1998), 137-156
DOI: 10.4064/sm-129-2-137-156
Streszczenie
If A generates a bounded cosine function on a Banach space X then the negative square root B of A generates a holomorphic semigroup, and this semigroup is the conjugate potential transform of the cosine function. This connection is studied in detail, and it is used for a characterization of cosine function generators in terms of growth conditions on the semigroup generated by B. The characterization relies on new results on the inversion of the vector-valued conjugate potential transform.
